Tacnode GUE-minor processes and double Aztec Diamonds

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <meta http-equiv="x-ua-compatible" content="ie=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <meta name="theme-color" content="#8e44ad"> <meta name="description" content="We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. A..." /> <meta name="robots" content="noarchive">  <meta name="citation_title" content="Tacnode GUE-minor processes and double Aztec Diamonds"> <meta name="citation_abstract" lang="en" content="We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, the natural limiting process is the GUE-minor process. Increasing the size of a double Aztec diamond while keeping the overlap between the two Aztec diamonds finite, we obtain a new determinantal point process which we call the tacnode GUE-minor process. This process can be thought of as two colliding GUE-minor processes. As part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode GUE-minor process, we find the inverse Kasteleyn matrix for the dimer model version of the Double Aztec diamond."> <meta name="citation_author" content="Adler, Mark"> <meta name="citation_author" content="Chhita, Sunil"> <meta name="citation_author" content="Johansson, Kurt"> <meta name="citation_author" content="van Moerbeke, Pierre"> <meta name="citation_publication_date" content="2014/07/25"> <meta name="citation_journal_title" content="Probability Theory and Related Fields"> <meta name="citation_volume" content="162"> <meta name="citation_issue" content="1"> <meta name="citation_doi" content="10.1007/s00440-014-0573-9"> <meta name="citation_publisher" content="Springer"> <meta name="citation_issn" content="0178-8051" /> <meta name="citation_issn" content="1432-2064" /> <meta name="citation_public_url" content="https://durham-repository.worktribe.com/output/1395522" /> <meta 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class="container"> <h1 class="title"> Tacnode GUE-minor processes and double Aztec Diamonds </h1> <h2 class="subtitle authors" style="margin-top: 1em;"> Adler, Mark; Chhita, Sunil; Johansson, Kurt; van Moerbeke, Pierre </h2> </div> </div> </header> <section class="section"> <div class="container"> <nav role="navigation" aria-label="Breadcrumbs" class="breadcrumb level"> <ul> <li> <a href="https://durham-repository.worktribe.com">Home</a> </li> <li> <a href="https://durham-repository.worktribe.com/outputs">Outputs</a> </li> </ul> </nav> <div class="columns"> <div class="column is-one-quarter"> <figure tabindex="0" role="button" class="image is-256x256" aria-label="View Preview" style="cursor: pointer;" onclick="$('[data-preview]').click();"> <img style="box-shadow: 0 1px 3px 0 rgba(0, 0, 0, 0.1), 0 1px 2px 0 rgba(0, 0, 0, 0.06);" src="https://durham-repository.worktribe.com/thumbnail/1395522" alt="Tacnode GUE-minor processes and double Aztec Diamonds Thumbnail" > </figure> <br /><br /> <h2 class="subtitle">Authors</h2> <div style="max-height: 100vh; overflow: auto;"> <article class="media"> <div class="media-content"> <div class="content"> <p> <strong>Mark Adler</strong> </p> </div> </div> </article> <article class="media"> <figure class="media-left"> <p class="image is-64x64"> <img src="https://durham-repository.worktribe.com/avatar/209870" alt="Profile image of Sunil Chhita"> </p> </figure> <div class="media-content"> <div class="content"> <p> <a href="https://durham-repository.worktribe.com/person/209870/sunil-chhita"><strong>Professor Sunil Chhita</strong></a> <small>sunil.chhita@durham.ac.uk</small> <br> Early Career Fellowship </p> </div> </div> <div class="media-right"> <a href="https://durham-repository.worktribe.com/person/209870/sunil-chhita" class="level-right" aria-label="Sunil Chhita"> <span class="icon is-small level-right"><i class="fa fa-info-circle" aria-hidden="true"></i></span> </a> </div> </article> <article class="media"> <div class="media-content"> <div class="content"> <p> <strong>Kurt Johansson</strong> </p> </div> </div> </article> <article class="media"> <div class="media-content"> <div class="content"> <p> <strong>Pierre van Moerbeke</strong> </p> </div> </div> </article> </div> <br /><br /> </div> <div class="column"> <div class="content abstract"> <h3 class="subtitle">Abstract</h3> <p class="description">We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, the natural limiting process is the GUE-minor process. Increasing the size of a double Aztec diamond while keeping the overlap between the two Aztec diamonds finite, we obtain a new determinantal point process which we call the tacnode GUE-minor process. This process can be thought of as two colliding GUE-minor processes. As part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode GUE-minor process, we find the inverse Kasteleyn matrix for the dimer model version of the Double Aztec diamond.</p> </div> <div class="content citation"> <h3 class="subtitle">Citation</h3> <p class="description"> Adler, M., Chhita, S., Johansson, K., & van Moerbeke, P. (2014). Tacnode GUE-minor processes and double Aztec Diamonds. Probability Theory and Related Fields, 162(1), 275-325. <a style="text-decoration: underline;" href="https://doi.org/10.1007/s00440-014-0573-9" target="_blank">https://doi.org/10.1007/s00440-014-0573-9</a> </p> </div> <table class="table" style="word-break: break-word; width:100%;"> <tbody> <tr> <th class="table-background" width="35%">Journal Article Type</th> <td>Article</td> </tr> <tr> <th class="table-background" width="35%">Acceptance Date</th> <td>May 23, 2014</td> </tr> <tr> <th class="table-background" width="35%">Online Publication Date</th> <td>Jul 25, 2014</td> </tr> <tr> <th class="table-background" width="35%">Publication Date</th> <td>Jul 25, 2014</td> </tr> <tr> <th class="table-background" width="35%">Deposit Date</th> <td>Oct 12, 2016</td> </tr> <tr> <th class="table-background" width="35%">Publicly Available Date</th> <td>Nov 24, 2016</td> </tr> <tr> <th class="table-background" width="35%">Journal</th> <td>Probability Theory and Related Fields</td> </tr> <tr> <th class="table-background" width="35%">Print ISSN</th> <td>0178-8051</td> </tr> <tr> <th class="table-background" width="35%">Electronic ISSN</th> <td>1432-2064</td> </tr> <tr> <th class="table-background" width="35%">Publisher</th> <td>Springer</td> </tr> <tr> <th class="table-background" width="35%">Peer Reviewed</th> <td>Peer Reviewed</td> </tr> <tr> <th class="table-background" width="35%">Volume</th> <td>162</td> </tr> <tr> <th class="table-background" width="35%">Issue</th> <td>1</td> </tr> <tr> <th class="table-background" width="35%">Pages</th> <td>275-325</td> </tr> <tr> <th class="table-background" width="35%">DOI</th> <td><a style="text-decoration: underline;" href="https://doi.org/10.1007/s00440-014-0573-9" target="_blank">https://doi.org/10.1007/s00440-014-0573-9</a></td> </tr> <tr> <th class="table-background" width="35%">Public URL</th> <td><a style="text-decoration: underline;" href="https://durham-repository.worktribe.com/output/1395522" 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<option value="1076691">Colleges</option> <option value="1076688">Colleges & Student Experience Division</option> <option value="1004335">Computing and Information Services</option> <option value="298099">Department of Accounting</option> <option value="155350">Department of Anthropology</option> <option value="155357">Department of Archaeology</option> <option value="155366">Department of Biosciences</option> <option value="155365">Department of Chemistry</option> <option value="155335">Department of Classics & Ancient History</option> <option value="155361">Department of Computer Science</option> <option value="155360">Department of Earth Sciences</option> <option value="840694">Department of Economics</option> <option value="155359">Department of Engineering</option> <option value="155342">Department of English Studies</option> <option value="840703">Department of Finance</option> <option value="155349">Department of Geography</option> <option value="155341">Department of 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<option value="298098">Faculty of Business</option> <option value="154059">Faculty of Science</option> <option value="154057">Faculty of Social Sciences and Health</option> <option value="1004350">Finance</option> <option value="1004349">Finance and Procurement Services</option> <option value="1076695">Global Engagement</option> <option value="1004355">Governance Support Services</option> <option value="1004337">HR & OD</option> <option value="1004348">International Office</option> <option value="1004356">Legal Services</option> <option value="1004338">Marketing and Communications</option> <option value="513681">Office of Vice Provost (Research)</option> <option value="1076689">PVC Colleges and Student Experience Office</option> <option value="1004352">PVC EDI Division</option> <option value="1004347">PVC Global Division</option> <option value="1004351">Procurement Services</option> <option value="1004334">Professional Services</option> <option value="1004332">Provost Division</option> <option value="1076692">Provost's Office</option> <option value="1076694">Recruitment and Admissions</option> <option value="155367">Research & Innovation Services</option> <option value="1076696">Research Institutes</option> <option value="155353">School of Education</option> <option value="155356">School of Government & International Affairs</option> <option value="155343">School of Modern Languages and Cultures</option> <option value="1004333">Strategic Planning & Insight Office</option> <option value="1076693">Strategy Delivery Unit</option> <option value="1076690">Student Support & Wellbeing Directorate</option> <option value="1004357">University Assurance Service</option> <option value="1004339">University Library and Collections</option> <option value="1004354">University Secretary</option> <option value="1004358">University Secretary's Office</option> <option value="1004359">Vice-Chancellor</option> <option value="1004360">Vice-Chancellor's Office</option> <option value="1004343">Vice-Provost Education Division</option> <option value="154060">Vice-Provost Research Division</option> </select> </div> </div>  <label for="type" class="label">Type</label> <div class="field"> <div class="select is-multiple control"> <select aria-label="Type" name="Type[]" id="type" multiple> <option value="Book">Book</option> <option value="Book Chapter">Book Chapter</option> <option value="Conference Proceeding">Conference Proceeding</option> <option value="Data">Data</option> <option value="Dataset">Dataset</option> <option value="Digital Artefact">Digital Artefact</option> <option value="Exhibition / Performance">Exhibition / Performance</option> <option value="Journal Article">Journal Article</option> <option value="Newspaper / Magazine">Newspaper / Magazine</option> <option value="Other">Other</option> <option value="Patent">Patent</option> <option value="Physical Artefact">Physical Artefact</option> <option value="Preprint / Working Paper">Preprint / Working Paper</option> <option value="Presentation / Conference">Presentation / Conference</option> <option value="Presentation / Conference Contribution">Presentation / Conference Contribution</option> <option value="Report">Report</option> <option value="Thesis">Thesis</option> <option value="Working Paper">Working Paper</option> </select> </div> </div>  <label for="publicationstatus" class="label">Publication Status</label> <div class="field"> <div class="select is-multiple control"> <select aria-label="Publication Status" name="PublicationStatus[]" id="publicationstatus" multiple> <option value="Submitted">Submitted</option> <option value="Accepted">Accepted</option> <option value="In Press">In Press</option> <option value="Published">Published</option> <option value="Unpublished">Unpublished</option> </select> </div> </div>  <label for="journal" class="label">Journal or Publication Title</label> <div class="field has-addons"> <p class="control"> <span class="select"> <select aria-label="Journal Operator" name="Journal_operator"> <option value="all">all of</option> <option value="any">any of</option> </select> </span> </p> <p class="control is-expanded"> <input aria-label="Journal or Publication Title" class="input" type="text" placeholder="Journal or Publication Title" name="Journal" id="journal" value=""> </p> </div>  <label for="order" class="label">Order the results</label> <div class="field"> <div class="control"> <div class="select" > <select aria-label="Order" name="order" id="order"> <option value="updated_atDesc">By last modified (most recent first)</option> <option value="updated_at">By last modified (oldest first)</option> <option value="ReportingDateDesc">By year (most recent first)</option> <option value="ReportingDate">By year (oldest first)</option> <option value="Title">By title</option> </select> </div> </div> </div> </form> </section> <div class="modal-card-foot"> <div class="field is-grouped"> <div class="control"> <button onclick="$('#advancedform').submit(); $(this).html('Searching').attr('disabled', true);" class="button is-link">Search</button> </div> </div> </div> </div> </div> <script src="/js/jquery-3.7.0.min.js"></script> <script src="/js/turbolinks.min.js"></script> <script> jQuery(document).ready(function ($) { $('html').css('overflow', 'auto'); var $toggle = $('#nav-toggle'); var $menu = $('#nav-menu'); $toggle.click(function() { $(this).toggleClass('is-active'); $menu.toggleClass('is-active'); }); $('.tree a').on('mouseover focus', function(e) { $.get($(this).attr("href"), function(data, status) { if (data.Description) { $('#org_info').show(); $('#org_title').text(data.Name); $('#org_desc').text(data.Description); } else { $('#org_info').hide(); } }); }); $('.navbar-link').focus(function() { var link = $(this); var dropdown = link.next('.navbar-dropdown'); dropdown.css('display', 'block'); dropdown.children().last().on('blur', function() { dropdown.attr('style', ''); }); }); 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