Critical percolation on random regular graphs

First published in Proc. Amer. Math. Soc. 146 (2018), 3321-3332, published by the American Mathematical Society

Detalles Bibliográficos
Autores: Joos, Felix, Perarnau Llobet, Guillem|||0000-0002-1953-9511
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/133720
Acceso en línea:https://hdl.handle.net/2117/133720
https://dx.doi.org/10.1090/proc/14021
Access Level:acceso abierto
Palabra clave:Graph theory
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
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spelling Critical percolation on random regular graphsJoos, FelixPerarnau Llobet, Guillem|||0000-0002-1953-9511Graph theoryGrafs, Teoria deÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafsFirst published in Proc. Amer. Math. Soc. 146 (2018), 3321-3332, published by the American Mathematical SocietyWe show that for all $ d\in \{3,\ldots ,n-1\}$ the size of the largest component of a random $ d$-regular graph on $ n$ vertices around the percolation threshold $ p=1/(d-1)$ is $ \Theta (n^{2/3})$, with high probability. This extends known results for fixed $ d\geq 3$ and for $ d=n-1$, confirming a prediction of Nachmias and Peres on a question of Benjamini. As a corollary, for the largest component of the percolated random $ d$-regular graph, we also determine the diameter and the mixing time of the lazy random walk. In contrast to previous approaches, our proof is based on a simple application of the switching method20182018-03-2020192019-05-30journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/133720https://dx.doi.org/10.1090/proc/14021reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1337202026-05-27T15:37:01Z
dc.title.none.fl_str_mv Critical percolation on random regular graphs
title Critical percolation on random regular graphs
spellingShingle Critical percolation on random regular graphs
Joos, Felix
Graph theory
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
title_short Critical percolation on random regular graphs
title_full Critical percolation on random regular graphs
title_fullStr Critical percolation on random regular graphs
title_full_unstemmed Critical percolation on random regular graphs
title_sort Critical percolation on random regular graphs
dc.creator.none.fl_str_mv Joos, Felix
Perarnau Llobet, Guillem|||0000-0002-1953-9511
author Joos, Felix
author_facet Joos, Felix
Perarnau Llobet, Guillem|||0000-0002-1953-9511
author_role author
author2 Perarnau Llobet, Guillem|||0000-0002-1953-9511
author2_role author
dc.subject.none.fl_str_mv Graph theory
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
topic Graph theory
Grafs, Teoria de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
description First published in Proc. Amer. Math. Soc. 146 (2018), 3321-3332, published by the American Mathematical Society
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-03-20
2019
2019-05-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/133720
https://dx.doi.org/10.1090/proc/14021
url https://hdl.handle.net/2117/133720
https://dx.doi.org/10.1090/proc/14021
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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