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dc.contributor.authorLabbé, Cyril
dc.contributor.authorLacoin, Hubert
dc.date.accessioned2019-02-19T08:55:25Z
dc.date.available2019-02-19T08:55:25Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18451
dc.language.isoenen
dc.subjectExclusion processen
dc.subjectWASEPen
dc.subjectMixing timeen
dc.subjectCutoffen
dc.subject.ddc519en
dc.titleMixing time and cutoff for the weakly asymmetric simple exclusion processen
dc.typeDocument de travail / Working paper
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.en
dc.identifier.citationpages39en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://arxiv.org/abs/1805.12213en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2018-06
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-02-19T08:53:22Z
hal.person.labIds60
hal.person.labIds87542


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