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The interchange process on high-dimensional products

hal.structure.identifier
dc.contributor.authorHermon, Jonathan
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSalez, Justin
HAL ID: 2772
dc.date.accessioned2021-03-24T10:16:38Z
dc.date.available2021-03-24T10:16:38Z
dc.date.issued2021-02
dc.identifier.issn1050-5164
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21654
dc.language.isoenen
dc.subjectcomparison of Dirichlet formsen
dc.subjectinterchange processen
dc.subjectMixing timesen
dc.subjectproduct graphsen
dc.subject.ddc519en
dc.titleThe interchange process on high-dimensional productsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe resolve a long-standing conjecture of Wilson (Ann. Appl. Probab.14 (2004) 274–325), reiterated by Oliveira (2016), asserting that the mixing time of the interchange process with unit edge rates on the n-dimensional hypercube is of order n. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order 1. Beyond the hypercube, our results apply to cartesian products of arbitrary graphs of fixed size, shedding light on a broad conjecture of Oliveira (Ann. Probab.41 (2013) 871–913).en
dc.relation.isversionofjnlnameAnnals of Applied Probability
dc.relation.isversionofjnlvol31en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2021-02
dc.relation.isversionofjnlpages84-98en
dc.relation.isversionofdoi10.1214/20-AAP1583en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidateouien
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-03-24T10:11:51Z
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