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Random walk on a perturbation of the infinitely-fast mixing interchange process

hal.structure.identifier
dc.contributor.authorSalvi, Michele*
hal.structure.identifier
dc.contributor.authorSimenhaus, François*
dc.date.accessioned2018-03-09T11:51:54Z
dc.date.available2018-03-09T11:51:54Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17528
dc.language.isoenen
dc.subjectRandom walk
dc.subjectdynamic random environment
dc.subjectinterchange process
dc.subjectlimit theorems
dc.subjectrenormalisation
dc.subject.ddc519en
dc.titleRandom walk on a perturbation of the infinitely-fast mixing interchange process
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider a random walk in dimension d ≥ 1 in a dynamic random environment evolving as an interchange process with rate γ > 0. We only assume that the annealed drift is non–zero. We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker Xt/ t eventually lies in an arbitrary small ball around the annealed drift. This statement is thus a perturbation of the case γ = +∞ where the environment is refreshed between each step of the walker. We extend three-way part of the results of [HS15], where the environment was given by the 1–dimensional exclusion process: (i) We deal with any dimension d ≥ 1; (ii) We treat the much more general interchange process, where each particle carries a transition vector chosen according to an arbitrary law µ; (iii) We show that X t t is not only in the same direction of the annealed drift, but that it is also close to it. AMS subject classification (2010 MSC): 60K37, 82C22, 60Fxx, 82D30.
dc.identifier.citationpages22
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01619895
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2018-07-23T08:51:11Z
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