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dc.contributor.authorEldan, Ronen
dc.contributor.authorLee, James
dc.contributor.authorLehec, Joseph
dc.date.accessioned2017-12-14T16:04:03Z
dc.date.available2017-12-14T16:04:03Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17231
dc.language.isoenen
dc.subjectMarkov chainsen
dc.subject.ddc519en
dc.titleTransport-entropy inequalities and curvature in discrete-space Markov chainsen
dc.typeChapitre d'ouvrage
dc.description.abstractenLet G = (Ω, E) be a graph and let d be the graph distance. Consider a discrete-time Markov chain {Z t } on Ω whose kernel p satisfies p(x, y) > 0 ⇒ {x, y} ∈ E for every x, y ∈ Ω. In words, transitions only occur between neighboring points of the graph. Suppose further that (Ω, p, d) has coarse Ricci curvature at least 1/α in the sense of Ollivier: For all x, y ∈ Ω, it holds that W 1 (Z 1 | {Z 0 = x}, Z 1 | {Z 0 = y}) ≤ 1 − 1 α d(x, y), where W 1 denotes the Wasserstein 1-distance. In this note, we derive a transport-entropy inequality: For any measure µ on Ω, it holds that W 1 (µ, π) ≤ √(2α/(2-1/α) D(µ ll π)) , where π denotes the stationary measure of {Z t } and D(·ll·) is the relative entropy. Peres and Tetali have conjectured a stronger consequence of coarse Ricci curvature, that a modified log-Sobolev inequality (MLSI) should hold, in analogy with the setting of Markov diffusions. We discuss how our approach suggests a natural attack on the MLSI conjecture.en
dc.identifier.citationpages391-406en
dc.relation.ispartoftitleA Journey Through Discrete Mathematics. A Tribute to Jiří Matoušeken
dc.relation.ispartofeditorLoebl, Martin
dc.relation.ispartofeditorNešetřil, Jaroslav
dc.relation.ispartofeditorThomas, Robin
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlin Heidelbergen
dc.relation.ispartofdate2017
dc.relation.ispartofurl10.1007/978-3-319-44479-6en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01428953en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.ispartofisbn978-3-319-44478-9en
dc.relation.forthcomingnonen
dc.identifier.doi10.1007/978-3-319-44479-6_16en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2017-10-25T09:42:42Z
hal.person.labIds6025
hal.person.labIds241505
hal.person.labIds60


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