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Hydrodynamic limit and cutoff for the biased adjacent walk on the simplex

hal.structure.identifierLaboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
dc.contributor.authorLabbé, Cyril
HAL ID: 9675
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPetit, Enguerand
dc.date.accessioned2022-11-07T15:53:03Z
dc.date.available2022-11-07T15:53:03Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23112
dc.language.isoenen
dc.subjectMixing timeen
dc.subjectCutoffen
dc.subjectAdjacent walken
dc.subjectHydrodynamic limiten
dc.subjectHamilton-Jacobi equationen
dc.subject.ddc519en
dc.titleHydrodynamic limit and cutoff for the biased adjacent walk on the simplexen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe investigate the asymptotic in N of the mixing times of a Markov dynamics on N−1 ordered particles in an interval. This dynamics consists in resampling at independent Poisson times each particle according to a probability measure on the segment formed by its nearest neighbours. In the setting where the resampling probability measures are symmetric, the asymptotic of the mixing times were obtained and a cutoff phenomenon holds. In the present work, we focus on an asymmetric version of the model and we establish a cutoff phenomenon. An important part of our analysis consists in the derivation of a hydrodynamic limit, which is given by a non-linear Hamilton-Jacobi equation with degenerate boundary conditions.en
dc.identifier.citationpages42en
dc.relation.ispartofseriestitleCahiers du CEREMADEen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-11-07T15:50:15Z
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