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hal.structure.identifierÉcole normale supérieure de Lyon [ENS de Lyon]
dc.contributor.authorBristiel, Alexandre
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSalez, Justin
HAL ID: 2772
dc.date.accessioned2023-01-16T12:09:28Z
dc.date.available2023-01-16T12:09:28Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23735
dc.language.isoenen
dc.subject.ddc519en
dc.titleSeparation cutoff for activated random walksen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider Activated Random Walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the non-reversibility of the dynamics and the lack of knowledge on the stationary distribution, we explicitly determine the relaxation time of the process, and prove that separation cutoff is equivalent to the product condition. We also provide sharp estimates on the center and width of the cutoff window. Finally, we illustrate those results by establishing explicit separation cutoffs on various networks, including: (i) large finite subgraphs of any fixed infinite non-amenable graph, with absorption at the boundary and (ii) large finite vertex-transitive graphs with absorption at a single vertex. The latter result settles a conjecture of Levine and Liang. Our proofs rely on the refined analysis of a strong stationary time recently discovered by Levine and Liang and involving the IDLA process.en
dc.publisher.cityParisen
dc.identifier.citationpages21en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2023-01-16T12:06:57Z
hal.author.functionaut
hal.author.functionaut


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