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Member of European Academy (2015),Priciple researcher at St.Petersburg branch of Mathematical Instituteof Russian Academy of Sciences.<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="53951142" href="https://www.academia.edu/Documents/in/Mathematics"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/AnatolyVershik","location":"/AnatolyVershik","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/AnatolyVershik","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" 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class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Anatoly M Vershik</h3></div><div class="js-work-strip profile--work_container" data-work-id="91434756"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434756/Central_measures_of_continuous_graded_graphs_the_case_of_distinct_frequencies"><img alt="Research paper thumbnail of Central measures of continuous graded graphs: the case of distinct frequencies" class="work-thumbnail" src="https://attachments.academia-assets.com/94723713/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434756/Central_measures_of_continuous_graded_graphs_the_case_of_distinct_frequencies">Central measures of continuous graded graphs: the case of distinct frequencies</a></div><div class="wp-workCard_item"><span>European Journal of Mathematics</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="83470e62a058c2f425ebdce5370cf0ae" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":94723713,"asset_id":91434756,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/94723713/download_file?st=MTczMjc5MTQ1NSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner 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The main observation is that an ergodic central measure on a subgraph of a Pascal-type graph can often be obtained as the restriction of the standard Bernoulli measure to the path space of the subgraph. This observation dramatically changes the approach to finding central measures also on discrete graphs, such as the famous Young graph. The simplest example of this type is given by the theorem on the weak limits of normalized Lebesgue measures on simplices; these are the so-called Cesàro measures, which are concentrated on the sequences with prescribed Cesàro limits (this limit parametrizes the corresponding measure). More complicated examples are the graphs of continuous Young diagrams with fixed number of rows and the graphs of spectra of infinite Hermitian matrices of finite rank. We prove existence and uniqueness theorems for ergodic central measures and describe their structure. In particular, our results 1) give a new spectral description of the so-called infinite-dimensional Wishart measures [15]-ergodic unitarily invariant measures of discrete type on the set of infinite Hermitian matrices; 2) describe the structure of continuous analogs of measures on discrete graded graphs. 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A. Berezi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis (&quot;supermathematics&quot;). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434743"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/91434743/Probability_Measures_in_Infinite_Dimensional_Spaces"><img alt="Research paper thumbnail of Probability Measures in Infinite-Dimensional Spaces" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/91434743/Probability_Measures_in_Infinite_Dimensional_Spaces">Probability Measures in Infinite-Dimensional Spaces</a></div><div class="wp-workCard_item"><span>Investigations in the Theory of Stochastic Processes</span><span>, 1971</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434743"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434743"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434743; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434734"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability"><img alt="Research paper thumbnail of Randomization of Algebra and Algebraization of Probability" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability">Randomization of Algebra and Algebraization of Probability</a></div><div class="wp-workCard_item"><span>Mathematics Unlimited — 2001 and Beyond</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is probably difficult to find areas of XIXth Century mathematics more remote from each other t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is probably difficult to find areas of XIXth Century mathematics more remote from each other than algebra, the foundation of mathematics, and probability theory, a semi-applied area perceived from the time of its emergence as an almost experimental science. 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Certainly, a number of its methods are specific to that science and were difficult to understand even 20 years ago. For example, specialists on differential equations were for a long time unable to assimilate techniques of stochastic calculus, although results obtained by probabilistic methods in the theory of equations competed successfully with theorems obtained by classical methods.","publication_date":{"day":null,"month":null,"year":2001,"errors":{}},"publication_name":"Mathematics Unlimited — 2001 and Beyond"},"translated_abstract":"It is probably difficult to find areas of XIXth Century mathematics more remote from each other than algebra, the foundation of mathematics, and probability theory, a semi-applied area perceived from the time of its emergence as an almost experimental science. We note, in passing, that in the works of P. L. Chebyshev’s students, A. A. Markov and A. M. Lyapunov, many assertions of probability theory (for example, the central limit theorem) were proved with complete rigour in great generality. Nevertheless, it is no accident that one of the famous problems, proposed by D. Hilbert involved axiomatization of mechanics and axiomatization of probability theory: at that time one could not assume that these areas were fully mathematicized. In the first half of the XXth Century the works of A. N. Kolmogorov, S. N. Bernstein, von Mises et al. created the foundations of probability theory, which were unconditionally accepted by the mathematical community, and all doubts about whether or not this was mathematics were removed. However, probability theory has retained a certain isolation until now. It is difficult to explain this rationally. Certainly, a number of its methods are specific to that science and were difficult to understand even 20 years ago. For example, specialists on differential equations were for a long time unable to assimilate techniques of stochastic calculus, although results obtained by probabilistic methods in the theory of equations competed successfully with theorems obtained by classical methods.","internal_url":"https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability","translated_internal_url":"","created_at":"2022-11-23T04:13:25.625-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Randomization_of_Algebra_and_Algebraization_of_Probability","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":344,"name":"Probability Theory","url":"https://www.academia.edu/Documents/in/Probability_Theory"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434728"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434728/A_nonholonomic_Laplace_operator"><img alt="Research paper thumbnail of A nonholonomic Laplace operator" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434728/A_nonholonomic_Laplace_operator">A nonholonomic Laplace operator</a></div><div class="wp-workCard_item"><span>Journal of Soviet Mathematics</span><span>, 1993</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defined in an invariant manner and its properties are considered. The method presented for studying it, as well as for the study of other hypoelliptic operators, involves the use of the geometry of nonholonomic manifolds. The nonholonomic metric (Carnot-Carathéodory metric), the Carathéodory measure, and hypoharmonic functions are defined. A theorem on the comparison of the spectra is proved and the connection is established between the bases of eigenfunctions of the ordinary and nonholonomic Laplacians. Conjectures are formulated on the principal term of the spectral asymptotic expansion of the nonholonomic Laplacian, on the structure of the wave fronts, and on the propagation of singularities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434728"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434728"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434728; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91434728]").text(description); $(".js-view-count[data-work-id=91434728]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91434728; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91434728']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 91434728, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=91434728]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91434728,"title":"A nonholonomic Laplace operator","translated_title":"","metadata":{"abstract":"In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defined in an invariant manner and its properties are considered. The method presented for studying it, as well as for the study of other hypoelliptic operators, involves the use of the geometry of nonholonomic manifolds. The nonholonomic metric (Carnot-Carathéodory metric), the Carathéodory measure, and hypoharmonic functions are defined. A theorem on the comparison of the spectra is proved and the connection is established between the bases of eigenfunctions of the ordinary and nonholonomic Laplacians. Conjectures are formulated on the principal term of the spectral asymptotic expansion of the nonholonomic Laplacian, on the structure of the wave fronts, and on the propagation of singularities.","publisher":"Springer Nature","publication_date":{"day":null,"month":null,"year":1993,"errors":{}},"publication_name":"Journal of Soviet Mathematics"},"translated_abstract":"In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defined in an invariant manner and its properties are considered. 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Conjectures are formulated on the principal term of the spectral asymptotic expansion of the nonholonomic Laplacian, on the structure of the wave fronts, and on the propagation of singularities.","internal_url":"https://www.academia.edu/91434728/A_nonholonomic_Laplace_operator","translated_internal_url":"","created_at":"2022-11-23T04:13:20.029-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"A_nonholonomic_Laplace_operator","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":529366,"name":"Soviet mathematics","url":"https://www.academia.edu/Documents/in/Soviet_mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434714"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434714/Product_of_commuting_spectral_measures_need_not_be_countably_additive"><img alt="Research paper thumbnail of Product of commuting spectral measures need not be countably additive" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434714/Product_of_commuting_spectral_measures_need_not_be_countably_additive">Product of commuting spectral measures need not be countably additive</a></div><div class="wp-workCard_item"><span>Functional Analysis and Its Applications</span><span>, 1979</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434714"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434714"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434714; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="85216660"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers"><img alt="Research paper thumbnail of Asymptotics of Young Diagrams and Hook Numbers" class="work-thumbnail" src="https://attachments.academia-assets.com/89983190/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers">Asymptotics of Young Diagrams and Hook Numbers</a></div><div class="wp-workCard_item"><span>The Electronic Journal of Combinatorics</span><span>, 1997</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Asymptotic calculations are applied to study the degrees of certain sequences of characters of sy...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\mu$, we deduce several skew diagrams which are related to $\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know &quot;finite&quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7ef4c4b64f42736c669e211a3dbd09d6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983190,"asset_id":85216660,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216660"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216660"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216660; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85216660]").text(description); $(".js-view-count[data-work-id=85216660]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85216660; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85216660']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 85216660, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7ef4c4b64f42736c669e211a3dbd09d6" } } $('.js-work-strip[data-work-id=85216660]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85216660,"title":"Asymptotics of Young Diagrams and Hook Numbers","translated_title":"","metadata":{"abstract":"Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\\mu$, we deduce several skew diagrams which are related to $\\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know \u0026quot;finite\u0026quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.","publisher":"The Electronic Journal of Combinatorics","publication_date":{"day":null,"month":null,"year":1997,"errors":{}},"publication_name":"The Electronic Journal of Combinatorics"},"translated_abstract":"Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\\mu$, we deduce several skew diagrams which are related to $\\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know \u0026quot;finite\u0026quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.","internal_url":"https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers","translated_internal_url":"","created_at":"2022-08-20T07:39:15.156-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":89983190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983190/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotics_of_Young_Diagrams_and_Hook_N.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983190/pdf-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotics_of_Young_Diagrams_and_Hook_N.pdf\u0026Expires=1732795055\u0026Signature=eAfkANGqlysYSLviEoWhGW-GIqh1wQgOklofWu2A3sFzbJpcLVZ9L7a2Am1Lp4FDwRR~~x4GcYqvzvPJIaY1KYuAAHvXizKRRDEt-tyEn5xfbRaDjqWpR8Cl-w85~fXG8ZkWZaZUmTLmec96-9eSyyzKwcIuQ187eFVOeKt8XOjZqqxm7GNaBFRmo9Zcc5NPO5uYDx0X4EsOyXZdZralT1OttJ2cZCy2RuRYF-58IEl50hZvQ1ozqU-zSR42-og0iOd5d7SPbVoVylfJpb-oc9csCV7w3QYtZaEg1EceSJRRJe~iDIlndlHY8ImHAeUMiuJUEMWAWJiT-eAbZVWOAw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Asymptotics_of_Young_Diagrams_and_Hook_Numbers","translated_slug":"","page_count":12,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[{"id":89983190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983190/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotics_of_Young_Diagrams_and_Hook_N.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983190/pdf-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotics_of_Young_Diagrams_and_Hook_N.pdf\u0026Expires=1732795056\u0026Signature=Ck5cYM8pgUFWJpT31q5gUTXxPbgG-1YVrhUeXp3ocqi7rTp-lXLnqQhz98qF6RCpGp8rorLlw570NcOFOi8T7Xd5QHCQQG6UL7OQ-iBxEfnwN6h6ncq~m2NbQeYjZwjShxlLvmUKQkNdYXA4fOS32qLo5FCIFG23JAzkmo519uf6hunNQ8UidhYd8w7~e3uvDZkFI37kkPgkAzrEoDGfiR0Txu~lnyTrYKd7xibaFXJ6Uo~P2~X-f7wnHeCFZl0BCJPfIweFmR40jgAklVd7xs5eVRCuHzWcdEz5JS8pVwEgCKsTs0qqePUc0Vg3idJr3ymf04gQw4SN1VmNmzxmJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":5436,"name":"Combinatorics","url":"https://www.academia.edu/Documents/in/Combinatorics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":135503,"name":"Partition","url":"https://www.academia.edu/Documents/in/Partition"},{"id":150408,"name":"Symmetric group","url":"https://www.academia.edu/Documents/in/Symmetric_group"},{"id":2123395,"name":"Hook","url":"https://www.academia.edu/Documents/in/Hook"},{"id":3663999,"name":"Asymptotic method","url":"https://www.academia.edu/Documents/in/Asymptotic_method"}],"urls":[{"id":23158994,"url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="85216659"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups"><img alt="Research paper thumbnail of The absolute of finitely generated groups: I. Commutative (semi)groups" class="work-thumbnail" src="https://attachments.academia-assets.com/89983188/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups">The absolute of finitely generated groups: I. Commutative (semi)groups</a></div><div class="wp-workCard_item"><span>European Journal of Mathematics</span><span>, 2018</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4953b110dd8dc7fb41101249bf6f95e7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983188,"asset_id":85216659,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216659"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216659"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216659; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85216659]").text(description); $(".js-view-count[data-work-id=85216659]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85216659; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85216659']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 85216659, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4953b110dd8dc7fb41101249bf6f95e7" } } $('.js-work-strip[data-work-id=85216659]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85216659,"title":"The absolute of finitely generated groups: I. Commutative (semi)groups","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"We give a complete description of the absolute of commutative finitely generated groups and semigroups. The absolute (previously called the exit boundary) is a further elaboration of the notion of the boundary of a random walk on a group (the Poisson-Furstenberg boundary); namely, the absolute of a (semi)group is the set of ergodic central measures on the compactum of all infinite trajectories of a simple random walk on the group. Related notions have been discussed in the probability literature: Martin boundary, entrance and exit boundaries (Dynkin), central measures on path spaces of graphs (Vershik-Kerov). A central measure (with respect to a finite system of generators of a group or semigroup) is a Markov measure on the space of trajectories whose cotransition distribution at every point is the uniform distribution on the generators (i. e., a measure of maximal entropy). For a more general notion of measures with a given cocycle, see [15]. For the group Z, the problem of describing the absolute is solved exactly by the classical de Finetti's theorem. The main result of this paper, which is a far-reaching generalization of de Finetti's theorem, is as follows: the absolute of a commutative semigroup coincides with the set of central measures corresponding to (nonstationary) Markov chains with independent identically distributed increments. Topologically, the absolute is (in the main case) a closed disk of finite dimension.","publication_date":{"day":null,"month":null,"year":2018,"errors":{}},"publication_name":"European Journal of Mathematics","grobid_abstract_attachment_id":89983188},"translated_abstract":null,"internal_url":"https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups","translated_internal_url":"","created_at":"2022-08-20T07:39:14.874-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":89983188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983188/thumbnails/1.jpg","file_name":"1801.02012v1.pdf","download_url":"https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_absolute_of_finitely_generated_group.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983188/1801.02012v1-libre.pdf?1661007326=\u0026response-content-disposition=attachment%3B+filename%3DThe_absolute_of_finitely_generated_group.pdf\u0026Expires=1732795056\u0026Signature=ZCPR-zxy1M9z9Hdi2XWpQcDHl8rzUoKnWlbH-HYAdL2tXlW5mJES1xPx0zD9tgA2TbXL2aErOY6efuZ-Dbspc9Jxb0IlTwJbW7MbSlx-OrMcIz8EJPudQjIxB37CfBrKSh0oMii2lsaz8OpqKyUKpT-BM5aE~kJXcSAxxh5UhQF6y4NnG~xso7miOFvLIQu4RnT2XWED7sgo-3i5wHdQjlOMk8ApwYzh95xlN-k3IicaY7vCa8Kah6FVEtX2HcsrhQy7bSh8QkzyGOr7T-5hm9EDlqy5U85pvKY5B8EwDelVJsKWymZsNE3DVISmUesI9etbp2mhyiYncQBiawa9hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups","translated_slug":"","page_count":16,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[{"id":89983188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983188/thumbnails/1.jpg","file_name":"1801.02012v1.pdf","download_url":"https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_absolute_of_finitely_generated_group.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983188/1801.02012v1-libre.pdf?1661007326=\u0026response-content-disposition=attachment%3B+filename%3DThe_absolute_of_finitely_generated_group.pdf\u0026Expires=1732795056\u0026Signature=ZCPR-zxy1M9z9Hdi2XWpQcDHl8rzUoKnWlbH-HYAdL2tXlW5mJES1xPx0zD9tgA2TbXL2aErOY6efuZ-Dbspc9Jxb0IlTwJbW7MbSlx-OrMcIz8EJPudQjIxB37CfBrKSh0oMii2lsaz8OpqKyUKpT-BM5aE~kJXcSAxxh5UhQF6y4NnG~xso7miOFvLIQu4RnT2XWED7sgo-3i5wHdQjlOMk8ApwYzh95xlN-k3IicaY7vCa8Kah6FVEtX2HcsrhQy7bSh8QkzyGOr7T-5hm9EDlqy5U85pvKY5B8EwDelVJsKWymZsNE3DVISmUesI9etbp2mhyiYncQBiawa9hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":346,"name":"Ergodic Theory","url":"https://www.academia.edu/Documents/in/Ergodic_Theory"},{"id":63969,"name":"Non-European roots of mathematics","url":"https://www.academia.edu/Documents/in/Non-European_roots_of_mathematics"},{"id":78086,"name":"Random Walk","url":"https://www.academia.edu/Documents/in/Random_Walk"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":23158993,"url":"http://link.springer.com/article/10.1007/s40879-018-0263-8/fulltext.html"}]}, dispatcherData: dispatcherData }); 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the Universal Adic Graph</a></div><div class="wp-workCard_item"><span>Functional Analysis and Its Applications</span><span>, 2018</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bf5c4f7bcd971b91236adab6d5bbe832" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983191,"asset_id":85216658,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983191/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216658"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216658"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216658; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="85216656"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/85216656/Special_Representations_of_the_Iwasawa_Subgroups_of_Simple_Lie_Groups"><img alt="Research paper thumbnail of Special Representations of the Iwasawa Subgroups of Simple Lie Groups" class="work-thumbnail" src="https://attachments.academia-assets.com/89983184/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/85216656/Special_Representations_of_the_Iwasawa_Subgroups_of_Simple_Lie_Groups">Special Representations of the Iwasawa Subgroups of Simple Lie Groups</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Sciences</span><span>, 2017</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45c09a10cff7a5de6ec7078d76104568" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983184,"asset_id":85216656,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983184/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216656"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216656"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216656; 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These subgroups are called the Iwasawa subgroups of the corresponding simple groups. The main property of these representations is the existence of nontrivial 1-cohomology with values in the representations. For groups of rank 1, the representations from this family are unitary; for ranks greater than 1, they are nonunitary. The paper continues a series of our previous papers and serves as an introduction to the theory of nonunitary current groups. 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The main observation is that an ergodic central measure on a subgraph of a Pascal-type graph can often be obtained as the restriction of the standard Bernoulli measure to the path space of the subgraph. This observation dramatically changes the approach to finding central measures also on discrete graphs, such as the famous Young graph. The simplest example of this type is given by the theorem on the weak limits of normalized Lebesgue measures on simplices; these are the so-called Cesàro measures, which are concentrated on the sequences with prescribed Cesàro limits (this limit parametrizes the corresponding measure). More complicated examples are the graphs of continuous Young diagrams with fixed number of rows and the graphs of spectra of infinite Hermitian matrices of finite rank. We prove existence and uniqueness theorems for ergodic central measures and describe their structure. 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A. Berezi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis (&quot;supermathematics&quot;). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434743"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/91434743/Probability_Measures_in_Infinite_Dimensional_Spaces"><img alt="Research paper thumbnail of Probability Measures in Infinite-Dimensional Spaces" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/91434743/Probability_Measures_in_Infinite_Dimensional_Spaces">Probability Measures in Infinite-Dimensional Spaces</a></div><div class="wp-workCard_item"><span>Investigations in the Theory of Stochastic Processes</span><span>, 1971</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434743"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434743"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434743; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91434743]").text(description); $(".js-view-count[data-work-id=91434743]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91434743; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91434743']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 91434743, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434734"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability"><img alt="Research paper thumbnail of Randomization of Algebra and Algebraization of Probability" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability">Randomization of Algebra and Algebraization of Probability</a></div><div class="wp-workCard_item"><span>Mathematics Unlimited — 2001 and Beyond</span><span>, 2001</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It is probably difficult to find areas of XIXth Century mathematics more remote from each other t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">It is probably difficult to find areas of XIXth Century mathematics more remote from each other than algebra, the foundation of mathematics, and probability theory, a semi-applied area perceived from the time of its emergence as an almost experimental science. We note, in passing, that in the works of P. L. Chebyshev’s students, A. A. Markov and A. M. Lyapunov, many assertions of probability theory (for example, the central limit theorem) were proved with complete rigour in great generality. Nevertheless, it is no accident that one of the famous problems, proposed by D. Hilbert involved axiomatization of mechanics and axiomatization of probability theory: at that time one could not assume that these areas were fully mathematicized. In the first half of the XXth Century the works of A. N. Kolmogorov, S. N. Bernstein, von Mises et al. created the foundations of probability theory, which were unconditionally accepted by the mathematical community, and all doubts about whether or not this was mathematics were removed. However, probability theory has retained a certain isolation until now. It is difficult to explain this rationally. Certainly, a number of its methods are specific to that science and were difficult to understand even 20 years ago. For example, specialists on differential equations were for a long time unable to assimilate techniques of stochastic calculus, although results obtained by probabilistic methods in the theory of equations competed successfully with theorems obtained by classical methods.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434734"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434734"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434734; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91434734]").text(description); $(".js-view-count[data-work-id=91434734]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91434734; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91434734']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 91434734, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=91434734]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91434734,"title":"Randomization of Algebra and Algebraization of Probability","translated_title":"","metadata":{"abstract":"It is probably difficult to find areas of XIXth Century mathematics more remote from each other than algebra, the foundation of mathematics, and probability theory, a semi-applied area perceived from the time of its emergence as an almost experimental science. 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Lyapunov, many assertions of probability theory (for example, the central limit theorem) were proved with complete rigour in great generality. Nevertheless, it is no accident that one of the famous problems, proposed by D. Hilbert involved axiomatization of mechanics and axiomatization of probability theory: at that time one could not assume that these areas were fully mathematicized. In the first half of the XXth Century the works of A. N. Kolmogorov, S. N. Bernstein, von Mises et al. created the foundations of probability theory, which were unconditionally accepted by the mathematical community, and all doubts about whether or not this was mathematics were removed. However, probability theory has retained a certain isolation until now. It is difficult to explain this rationally. Certainly, a number of its methods are specific to that science and were difficult to understand even 20 years ago. For example, specialists on differential equations were for a long time unable to assimilate techniques of stochastic calculus, although results obtained by probabilistic methods in the theory of equations competed successfully with theorems obtained by classical methods.","internal_url":"https://www.academia.edu/91434734/Randomization_of_Algebra_and_Algebraization_of_Probability","translated_internal_url":"","created_at":"2022-11-23T04:13:25.625-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Randomization_of_Algebra_and_Algebraization_of_Probability","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":344,"name":"Probability Theory","url":"https://www.academia.edu/Documents/in/Probability_Theory"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434728"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434728/A_nonholonomic_Laplace_operator"><img alt="Research paper thumbnail of A nonholonomic Laplace operator" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434728/A_nonholonomic_Laplace_operator">A nonholonomic Laplace operator</a></div><div class="wp-workCard_item"><span>Journal of Soviet Mathematics</span><span>, 1993</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defined in an invariant manner and its properties are considered. The method presented for studying it, as well as for the study of other hypoelliptic operators, involves the use of the geometry of nonholonomic manifolds. The nonholonomic metric (Carnot-Carathéodory metric), the Carathéodory measure, and hypoharmonic functions are defined. A theorem on the comparison of the spectra is proved and the connection is established between the bases of eigenfunctions of the ordinary and nonholonomic Laplacians. Conjectures are formulated on the principal term of the spectral asymptotic expansion of the nonholonomic Laplacian, on the structure of the wave fronts, and on the propagation of singularities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434728"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434728"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434728; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=91434728]").text(description); $(".js-view-count[data-work-id=91434728]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 91434728; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='91434728']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 91434728, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=91434728]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":91434728,"title":"A nonholonomic Laplace operator","translated_title":"","metadata":{"abstract":"In this paper first the Laplace operator on a completely nonholonomic Riemannian manifold is defined in an invariant manner and its properties are considered. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="91434714"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/91434714/Product_of_commuting_spectral_measures_need_not_be_countably_additive"><img alt="Research paper thumbnail of Product of commuting spectral measures need not be countably additive" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/91434714/Product_of_commuting_spectral_measures_need_not_be_countably_additive">Product of commuting spectral measures need not be countably additive</a></div><div class="wp-workCard_item"><span>Functional Analysis and Its Applications</span><span>, 1979</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="91434714"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="91434714"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 91434714; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="85216660"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers"><img alt="Research paper thumbnail of Asymptotics of Young Diagrams and Hook Numbers" class="work-thumbnail" src="https://attachments.academia-assets.com/89983190/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers">Asymptotics of Young Diagrams and Hook Numbers</a></div><div class="wp-workCard_item"><span>The Electronic Journal of Combinatorics</span><span>, 1997</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Asymptotic calculations are applied to study the degrees of certain sequences of characters of sy...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\mu$, we deduce several skew diagrams which are related to $\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know &quot;finite&quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7ef4c4b64f42736c669e211a3dbd09d6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983190,"asset_id":85216660,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216660"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216660"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216660; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85216660]").text(description); $(".js-view-count[data-work-id=85216660]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85216660; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85216660']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 85216660, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7ef4c4b64f42736c669e211a3dbd09d6" } } $('.js-work-strip[data-work-id=85216660]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85216660,"title":"Asymptotics of Young Diagrams and Hook Numbers","translated_title":"","metadata":{"abstract":"Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\\mu$, we deduce several skew diagrams which are related to $\\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know \u0026quot;finite\u0026quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.","publisher":"The Electronic Journal of Combinatorics","publication_date":{"day":null,"month":null,"year":1997,"errors":{}},"publication_name":"The Electronic Journal of Combinatorics"},"translated_abstract":"Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\\mu$, we deduce several skew diagrams which are related to $\\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know \u0026quot;finite\u0026quot;, nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.","internal_url":"https://www.academia.edu/85216660/Asymptotics_of_Young_Diagrams_and_Hook_Numbers","translated_internal_url":"","created_at":"2022-08-20T07:39:15.156-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":89983190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983190/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotics_of_Young_Diagrams_and_Hook_N.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983190/pdf-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotics_of_Young_Diagrams_and_Hook_N.pdf\u0026Expires=1732795055\u0026Signature=eAfkANGqlysYSLviEoWhGW-GIqh1wQgOklofWu2A3sFzbJpcLVZ9L7a2Am1Lp4FDwRR~~x4GcYqvzvPJIaY1KYuAAHvXizKRRDEt-tyEn5xfbRaDjqWpR8Cl-w85~fXG8ZkWZaZUmTLmec96-9eSyyzKwcIuQ187eFVOeKt8XOjZqqxm7GNaBFRmo9Zcc5NPO5uYDx0X4EsOyXZdZralT1OttJ2cZCy2RuRYF-58IEl50hZvQ1ozqU-zSR42-og0iOd5d7SPbVoVylfJpb-oc9csCV7w3QYtZaEg1EceSJRRJe~iDIlndlHY8ImHAeUMiuJUEMWAWJiT-eAbZVWOAw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Asymptotics_of_Young_Diagrams_and_Hook_Numbers","translated_slug":"","page_count":12,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[{"id":89983190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983190/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/89983190/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotics_of_Young_Diagrams_and_Hook_N.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983190/pdf-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotics_of_Young_Diagrams_and_Hook_N.pdf\u0026Expires=1732795056\u0026Signature=Ck5cYM8pgUFWJpT31q5gUTXxPbgG-1YVrhUeXp3ocqi7rTp-lXLnqQhz98qF6RCpGp8rorLlw570NcOFOi8T7Xd5QHCQQG6UL7OQ-iBxEfnwN6h6ncq~m2NbQeYjZwjShxlLvmUKQkNdYXA4fOS32qLo5FCIFG23JAzkmo519uf6hunNQ8UidhYd8w7~e3uvDZkFI37kkPgkAzrEoDGfiR0Txu~lnyTrYKd7xibaFXJ6Uo~P2~X-f7wnHeCFZl0BCJPfIweFmR40jgAklVd7xs5eVRCuHzWcdEz5JS8pVwEgCKsTs0qqePUc0Vg3idJr3ymf04gQw4SN1VmNmzxmJw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":5436,"name":"Combinatorics","url":"https://www.academia.edu/Documents/in/Combinatorics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":135503,"name":"Partition","url":"https://www.academia.edu/Documents/in/Partition"},{"id":150408,"name":"Symmetric group","url":"https://www.academia.edu/Documents/in/Symmetric_group"},{"id":2123395,"name":"Hook","url":"https://www.academia.edu/Documents/in/Hook"},{"id":3663999,"name":"Asymptotic method","url":"https://www.academia.edu/Documents/in/Asymptotic_method"}],"urls":[{"id":23158994,"url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="85216659"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups"><img alt="Research paper thumbnail of The absolute of finitely generated groups: I. Commutative (semi)groups" class="work-thumbnail" src="https://attachments.academia-assets.com/89983188/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups">The absolute of finitely generated groups: I. Commutative (semi)groups</a></div><div class="wp-workCard_item"><span>European Journal of Mathematics</span><span>, 2018</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4953b110dd8dc7fb41101249bf6f95e7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983188,"asset_id":85216659,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216659"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216659"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216659; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85216659]").text(description); $(".js-view-count[data-work-id=85216659]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85216659; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85216659']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 85216659, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4953b110dd8dc7fb41101249bf6f95e7" } } $('.js-work-strip[data-work-id=85216659]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85216659,"title":"The absolute of finitely generated groups: I. Commutative (semi)groups","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"We give a complete description of the absolute of commutative finitely generated groups and semigroups. The absolute (previously called the exit boundary) is a further elaboration of the notion of the boundary of a random walk on a group (the Poisson-Furstenberg boundary); namely, the absolute of a (semi)group is the set of ergodic central measures on the compactum of all infinite trajectories of a simple random walk on the group. Related notions have been discussed in the probability literature: Martin boundary, entrance and exit boundaries (Dynkin), central measures on path spaces of graphs (Vershik-Kerov). A central measure (with respect to a finite system of generators of a group or semigroup) is a Markov measure on the space of trajectories whose cotransition distribution at every point is the uniform distribution on the generators (i. e., a measure of maximal entropy). For a more general notion of measures with a given cocycle, see [15]. For the group Z, the problem of describing the absolute is solved exactly by the classical de Finetti's theorem. The main result of this paper, which is a far-reaching generalization of de Finetti's theorem, is as follows: the absolute of a commutative semigroup coincides with the set of central measures corresponding to (nonstationary) Markov chains with independent identically distributed increments. Topologically, the absolute is (in the main case) a closed disk of finite dimension.","publication_date":{"day":null,"month":null,"year":2018,"errors":{}},"publication_name":"European Journal of Mathematics","grobid_abstract_attachment_id":89983188},"translated_abstract":null,"internal_url":"https://www.academia.edu/85216659/The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups","translated_internal_url":"","created_at":"2022-08-20T07:39:14.874-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":89983188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983188/thumbnails/1.jpg","file_name":"1801.02012v1.pdf","download_url":"https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_absolute_of_finitely_generated_group.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983188/1801.02012v1-libre.pdf?1661007326=\u0026response-content-disposition=attachment%3B+filename%3DThe_absolute_of_finitely_generated_group.pdf\u0026Expires=1732795056\u0026Signature=ZCPR-zxy1M9z9Hdi2XWpQcDHl8rzUoKnWlbH-HYAdL2tXlW5mJES1xPx0zD9tgA2TbXL2aErOY6efuZ-Dbspc9Jxb0IlTwJbW7MbSlx-OrMcIz8EJPudQjIxB37CfBrKSh0oMii2lsaz8OpqKyUKpT-BM5aE~kJXcSAxxh5UhQF6y4NnG~xso7miOFvLIQu4RnT2XWED7sgo-3i5wHdQjlOMk8ApwYzh95xlN-k3IicaY7vCa8Kah6FVEtX2HcsrhQy7bSh8QkzyGOr7T-5hm9EDlqy5U85pvKY5B8EwDelVJsKWymZsNE3DVISmUesI9etbp2mhyiYncQBiawa9hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_absolute_of_finitely_generated_groups_I_Commutative_semi_groups","translated_slug":"","page_count":16,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[{"id":89983188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983188/thumbnails/1.jpg","file_name":"1801.02012v1.pdf","download_url":"https://www.academia.edu/attachments/89983188/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_absolute_of_finitely_generated_group.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983188/1801.02012v1-libre.pdf?1661007326=\u0026response-content-disposition=attachment%3B+filename%3DThe_absolute_of_finitely_generated_group.pdf\u0026Expires=1732795056\u0026Signature=ZCPR-zxy1M9z9Hdi2XWpQcDHl8rzUoKnWlbH-HYAdL2tXlW5mJES1xPx0zD9tgA2TbXL2aErOY6efuZ-Dbspc9Jxb0IlTwJbW7MbSlx-OrMcIz8EJPudQjIxB37CfBrKSh0oMii2lsaz8OpqKyUKpT-BM5aE~kJXcSAxxh5UhQF6y4NnG~xso7miOFvLIQu4RnT2XWED7sgo-3i5wHdQjlOMk8ApwYzh95xlN-k3IicaY7vCa8Kah6FVEtX2HcsrhQy7bSh8QkzyGOr7T-5hm9EDlqy5U85pvKY5B8EwDelVJsKWymZsNE3DVISmUesI9etbp2mhyiYncQBiawa9hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":346,"name":"Ergodic Theory","url":"https://www.academia.edu/Documents/in/Ergodic_Theory"},{"id":63969,"name":"Non-European roots of mathematics","url":"https://www.academia.edu/Documents/in/Non-European_roots_of_mathematics"},{"id":78086,"name":"Random Walk","url":"https://www.academia.edu/Documents/in/Random_Walk"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":23158993,"url":"http://link.springer.com/article/10.1007/s40879-018-0263-8/fulltext.html"}]}, dispatcherData: dispatcherData }); 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the Universal Adic Graph</a></div><div class="wp-workCard_item"><span>Functional Analysis and Its Applications</span><span>, 2018</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bf5c4f7bcd971b91236adab6d5bbe832" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":89983191,"asset_id":85216658,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/89983191/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216658"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216658"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216658; 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In turn, the notion of combinatorial scheme is a source of new metric invariants of automorphisms approximated via basic filtrations. We construct a universal graph endowed with an adic structure such that every automorphism can be realized in its path space.","publication_date":{"day":null,"month":null,"year":2018,"errors":{}},"publication_name":"Functional Analysis and Its Applications","grobid_abstract_attachment_id":89983191},"translated_abstract":null,"internal_url":"https://www.academia.edu/85216658/Combinatorial_Invariants_of_Metric_Filtrations_and_Automorphisms_the_Universal_Adic_Graph","translated_internal_url":"","created_at":"2022-08-20T07:39:14.624-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":53951142,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":89983191,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983191/thumbnails/1.jpg","file_name":"1812.07841v1.pdf","download_url":"https://www.academia.edu/attachments/89983191/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Combinatorial_Invariants_of_Metric_Filtr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983191/1812.07841v1-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DCombinatorial_Invariants_of_Metric_Filtr.pdf\u0026Expires=1732795056\u0026Signature=H7~l7jJ9eVinxwWL2vtyJ9hD~bxtwAlFPw-lrrZRfyxxCRF6nsBDLb8Q3f4j6NxqZ-hgNjU1RIUQlQTErhb0-Ps0Egg9Oqhulmzio2XT4Nll2BXY9Qq9nqBg54IsB7H~6Cd9V4sGk7RhpFFkGNMoeJG-v6KMRD6oX4gYgw3M0BNJd4Ih~IUqC0LYuT1kTbo1N-n~IFLMtY~D4z2LsBmET2szxtX3RrsfKEGY8BVwiyvj1eunc74f-9haw0FGf4b3mvWkhX7KsOdqy~QP~S0qsdU8mNeiQzlN8esQt60t99Gf0kFWQE87RM8NOlQcz2DDMCyCW6pVguwC4SJ-EeOmVw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Combinatorial_Invariants_of_Metric_Filtrations_and_Automorphisms_the_Universal_Adic_Graph","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":53951142,"first_name":"Anatoly","middle_initials":"M","last_name":"Vershik","page_name":"AnatolyVershik","domain_name":"independent","created_at":"2016-09-24T21:54:16.311-07:00","display_name":"Anatoly M Vershik","url":"https://independent.academia.edu/AnatolyVershik"},"attachments":[{"id":89983191,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/89983191/thumbnails/1.jpg","file_name":"1812.07841v1.pdf","download_url":"https://www.academia.edu/attachments/89983191/download_file?st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&st=MTczMjc5MTQ1Niw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Combinatorial_Invariants_of_Metric_Filtr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/89983191/1812.07841v1-libre.pdf?1661007324=\u0026response-content-disposition=attachment%3B+filename%3DCombinatorial_Invariants_of_Metric_Filtr.pdf\u0026Expires=1732795056\u0026Signature=H7~l7jJ9eVinxwWL2vtyJ9hD~bxtwAlFPw-lrrZRfyxxCRF6nsBDLb8Q3f4j6NxqZ-hgNjU1RIUQlQTErhb0-Ps0Egg9Oqhulmzio2XT4Nll2BXY9Qq9nqBg54IsB7H~6Cd9V4sGk7RhpFFkGNMoeJG-v6KMRD6oX4gYgw3M0BNJd4Ih~IUqC0LYuT1kTbo1N-n~IFLMtY~D4z2LsBmET2szxtX3RrsfKEGY8BVwiyvj1eunc74f-9haw0FGf4b3mvWkhX7KsOdqy~QP~S0qsdU8mNeiQzlN8esQt60t99Gf0kFWQE87RM8NOlQcz2DDMCyCW6pVguwC4SJ-EeOmVw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":23158992,"url":"http://link.springer.com/article/10.1007/s10688-018-0236-1/fulltext.html"}]}, dispatcherData: dispatcherData }); 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A generalization of the RSK algorithm leads to a combinatorial interpretation of extended Schur functions. Applications are given to Ulam’s problem on longest increasing subsequences and to a law of large numbers for representations. 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Configurational topology studies topological spaces as configuration spaces, spaces of optimization problems etc. A more detailed description of the whole spectrum of these questions is to be published soon (see also [2,3,7] ).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="85216653"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85216653"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85216653; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85216653]").text(description); $(".js-view-count[data-work-id=85216653]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85216653; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85216653']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 85216653, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=85216653]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85216653,"title":"On topological questions of real complexity theory and combinatorial optimization","translated_title":"","metadata":{"abstract":"In this paper we continue the line started in ~,2,3] and formulate a ~umber of problems of the real complexity theory and combinatorial optimization as the problems investigating the properties of sequences of semialgebraic sets, their singularities, boundaries etc. The main idea is to apply the methods of real analysis and singularity theory to the study of spaces of problems and to treat the main notions of complexity theory (P, NP, NP-completeness and others) as the complexity of different spectra of semialgebraic sets. 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