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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

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1905.02146.pdf (229.6Kb)
Type
Article accepté pour publication ou publié
Date
2021-02
Journal name
Annals of Applied Probability
Volume
31
Number
1
Publisher
Institute of Mathematical Statistics
Pages
84-98
Publication identifier
10.1214/20-AAP1583
Metadata
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Author(s)
Hermon, Jonathan

Salez, Justin
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 / Keywords
comparison of Dirichlet forms; interchange process; Mixing times; product graphs

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