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
Department of mathematics, University of British Columbia
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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