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(PDF) Percolation on Fractal Networks: A Survey | Alexander Balankin - Academia.edu
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Some challenging questions are outlined.","author":[{"@context":"https://schema.org","@type":"Person","name":"Alexander Balankin"}],"contributor":[],"dateCreated":"2023-12-31","dateModified":"2024-01-22","datePublished":"2023-03-05","headline":"Percolation on Fractal Networks: A Survey","inLanguage":"en","keywords":["Statistical Physics","Fractal"],"locationCreated":null,"publication":"Fractal and fractional","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Multidisciplinary Digital Publishing Institute"},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/112693132/Percolation_on_Fractal_Networks_A_Survey","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-102fa537001ba4d8dcd921ad9bd56c474abc201906ea4843e7e7efe9dfbf561d.css" /><link rel="stylesheet" media="all" 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data-entity-id="69177732" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation">Fat fractal percolation and k-fractal percolation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="52848710" href="https://independent.academia.edu/FedericoCamia">Federico Camia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Latin American journal of probability and mathematical statistics</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider two variations on the Mandelbrot fractal percolation model. In the k-fractal percolation model, the d-dimensional unit cube is divided in N^d equal subcubes, k of which are retained while the others are discarded. The procedure is then iterated inside the retained cubes at all smaller scales. We show that the (properly rescaled) percolation critical value of this model converges to the critical value of ordinary site percolation on a particular d-dimensional lattice as N tends to infinity. This is analogous to the result of Falconer and Grimmett that the critical value for Mandelbrot fractal percolation converges to the critical value of site percolation on the same d-dimensional lattice. In the fat fractal percolation model, subcubes are retained with probability p_n at step n of the construction, where (p_n) is a non-decreasing sequence with \prod p_n &gt; 0. The Lebesgue measure of the limit set is positive a.s. given non-extinction. We prove that either the set of co...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fat fractal percolation and k-fractal percolation","attachmentId":79372658,"attachmentType":"pdf","work_url":"https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/69177732/Fat_fractal_percolation_and_k_fractal_percolation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":109843759,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":109843759,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_109843759" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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Havlin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Diffusion and fracton dimensionality on fractals and on percolation clusters","attachmentId":82317053,"attachmentType":"pdf","work_url":"https://www.academia.edu/74007298/Diffusion_and_fracton_dimensionality_on_fractals_and_on_percolation_clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/74007298/Diffusion_and_fracton_dimensionality_on_fractals_and_on_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="4467161" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks">Thermodynamics of fractal networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3723086" href="https://cnr-it.academia.edu/francescacolaiori">Francesca Colaiori</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Thermodynamics of fractal networks","attachmentId":31875273,"attachmentType":"pdf","work_url":"https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/4467161/Thermodynamics_of_fractal_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="26525698" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26525698/II_Territory_covered_by_N_random_walkers_on_stochastic_fractals_The_percolation_aggregate">II. Territory covered by N random walkers on stochastic fractals. The percolation aggregate</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50493670" href="https://upv-es.academia.edu/LuisAcedo">Luis Acedo</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"II. Territory covered by N random walkers on stochastic fractals. 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Vannimenus</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal de Physique Lettres, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On intrinsic properties of fractal lattices and percolation clusters","attachmentId":87708010,"attachmentType":"pdf","work_url":"https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/81783435/On_intrinsic_properties_of_fractal_lattices_and_percolation_clusters"><span class="ds2-5-text-link__content">View PDF</span><span 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href="https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals">Percolation on infinitely ramified fractals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="136645528" href="https://independent.academia.edu/DavidMovshovitz">David Movshovitz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on infinitely ramified fractals","attachmentId":67567229,"attachmentType":"pdf","work_url":"https://www.academia.edu/49182700/Percolation_on_infinitely_ramified_fractals","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free 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class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Fractal dimension and correlations in percolation theory","attachmentId":39948825,"attachmentType":"pdf","work_url":"https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/18237064/On_the_Fractal_dimension_and_correlations_in_percolation_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" 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data-entity-id="17420214" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17420214/Conductivity_measurement_on_percolation_fractal">Conductivity measurement on percolation fractal</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37146797" href="https://independent.academia.edu/AlexanderPalevski">Alexander Palevski</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Conductivity measurement on percolation fractal","attachmentId":42261347,"attachmentType":"pdf","work_url":"https://www.academia.edu/17420214/Conductivity_measurement_on_percolation_fractal","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://blogspot.academia.edu/RiccardoRigon">Riccardo Rigon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Water Resources Research, 1991</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Note on Fractal Channel Networks","attachmentId":49243972,"attachmentType":"pdf","work_url":"https://www.academia.edu/5557037/A_Note_on_Fractal_Channel_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5557037/A_Note_on_Fractal_Channel_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://www.academia.edu/32428505/Percolation_on_a_multifractal_scale_free_planar_stochastic_lattice_and_its_universality_class">Percolation on a multifractal scale-free planar stochastic lattice and its universality class</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62710135" href="https://independent.academia.edu/kamrulHossain8">Kamrul Hassan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Percolation on a multifractal scale-free planar stochastic lattice and its universality 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