dc.contributor.author Eldan, Ronen dc.contributor.author Lee, James dc.contributor.author Lehec, Joseph dc.date.accessioned 2017-12-14T16:04:03Z dc.date.available 2017-12-14T16:04:03Z dc.date.issued 2017 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/17231 dc.language.iso en en dc.subject Markov chains en dc.subject.ddc 519 en dc.title Transport-entropy inequalities and curvature in discrete-space Markov chains en dc.type Chapitre d'ouvrage dc.description.abstracten Let 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.citationpages 391-406 en dc.relation.ispartoftitle A Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek en dc.relation.ispartofeditor Loebl, Martin dc.relation.ispartofeditor Nešetřil, Jaroslav dc.relation.ispartofeditor Thomas, Robin dc.relation.ispartofpublname Springer en dc.relation.ispartofpublcity Berlin Heidelberg en dc.relation.ispartofdate 2017 dc.relation.ispartofurl 10.1007/978-3-319-44479-6 en dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-01428953 en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.relation.ispartofisbn 978-3-319-44478-9 en dc.relation.forthcoming non en dc.identifier.doi 10.1007/978-3-319-44479-6_16 en dc.description.ssrncandidate non en dc.description.halcandidate non en dc.description.readership recherche en dc.description.audience International en dc.date.updated 2017-10-25T09:42:42Z hal.person.labIds 6025 hal.person.labIds 241505 hal.person.labIds 60
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.