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Mixing time of the adjacent walk on the simplex

hal.structure.identifierDipartimento di Matematica [Roma TRE]
dc.contributor.authorCaputo, Pietro
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLabbé, Cyril
HAL ID: 9675
hal.structure.identifierInstituto Nacional de Matemática Pura e Aplicada [IMPA]
dc.contributor.authorLacoin, Hubert
dc.date.accessioned2021-12-07T09:03:32Z
dc.date.available2021-12-07T09:03:32Z
dc.date.issued2020
dc.identifier.issn2168-894X
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22328
dc.language.isoenen
dc.subjectadjacent walken
dc.subjectCutoffen
dc.subjectmixing timeen
dc.subjectspectral gapen
dc.subject.ddc519en
dc.titleMixing time of the adjacent walk on the simplexen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenBy viewing the N-simplex as the set of positions of N−1 ordered particles on the unit interval, the adjacent walk is the continuous-time Markov chain obtained by updating independently at rate 1 the position of each particle with a sample from the uniform distribution over the interval given by the two particles adjacent to it. We determine its spectral gap and prove that both the total variation distance and the separation distance to the uniform distribution exhibit a cutoff phenomenon, with mixing times that differ by a factor 2. The results are extended to the family of log-concave distributions obtained by replacing the uniform sampling by a symmetric log-concave Beta distributionen
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol48en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2020-09
dc.relation.isversionofjnlpages2449-2493en
dc.relation.isversionofdoi10.1214/20-AOP1428en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-12-07T09:00:11Z
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hal.author.functionaut
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