The interchange process on high-dimensional products
Hermon, Jonathan; Salez, Justin (2021), The interchange process on high-dimensional products, Annals of Applied Probability, 31, 1, p. 84-98. 10.1214/20-AAP1583
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Applied Probability
Institute of Mathematical Statistics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We resolve a long-standing conjecture of Wilson (Ann. Appl. Probab.14 (2004) 274–325), reiterated by Oliveira (2016), asserting that the mixing time of the interchange process with unit edge rates on the n-dimensional hypercube is of order n. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order 1. Beyond the hypercube, our results apply to cartesian products of arbitrary graphs of fixed size, shedding light on a broad conjecture of Oliveira (Ann. Probab.41 (2013) 871–913).
Subjects / Keywordscomparison of Dirichlet forms; interchange process; Mixing times; product graphs
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