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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLabbé, Cyril
hal.structure.identifierInstituto Nacional de Matemática Pura e Aplicada [IMPA]
dc.contributor.authorLacoin, Hubert
dc.date.accessioned2019-02-19T08:55:25Z
dc.date.available2019-02-19T08:55:25Z
dc.date.issued2020
dc.identifier.issn1050-5164
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18451
dc.language.isoenen
dc.subjectExclusion process
dc.subjectWASEP
dc.subjectMixing time
dc.subjectCutoff
dc.subject.ddc519en
dc.titleMixing time and cutoff for the weakly asymmetric simple exclusion process
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the simple exclusion process with k particles on a segment of length N performing random walks with transition p>1/2 to the right and q=1−p to the left. We focus on the case where the asymmetry in the jump rates b=p−q>0 vanishes in the limit when N and k tend to infinity, and obtain sharp asymptotics for the mixing times of this sequence of Markov chains in the two cases where the asymmetry is either much larger or much smaller than (logk)/N. We show that in the former case (b≫(logk)/N), the mixing time corresponds to the time needed to reach macroscopic equilibrium, like for the strongly asymmetric (i.e.\ constant b) case studied in [LL18], while the latter case (b≪(logk)/N) macroscopic equilibrium is not sufficient for mixing and one must wait till local fluctuations equilibrate, similarly to what happens in the symmetric case worked out in [Lac16b]. In both cases, convergence to equilibrium is abrupt: we have a cutoff phenomenon for the total-variation distance. We present a conjecture for the remaining regime when the asymmetry is of order (logk)/N.
dc.relation.isversionofjnlnameAnnals of Applied Probability
dc.relation.isversionofjnlvol30
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages1847-1883
dc.relation.isversionofdoi10.1214/19-AAP1545
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-23T08:52:19Z
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