Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion
Lacoin, Hubert (2016), Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion, Annals of Probability, 44, 2, p. 1426-1487. 10.1214/15-AOP1004
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Probability
Institute of Mathematical Statistics
MetadataShow full item record
Abstract (EN)In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of cards. We prove that around time N^2\log N/(2\pi^2), the total-variation distance to equilibrium of the deck distribution drops abruptly from 1 to 0, and that the separation distance has a similar behavior but with a transition occurring at time (N^2\log N)/\pi^2. This solves a conjecture formulated by David Wilson. We present also similar results for the exclusion process on a segment of length N with k particles.
Subjects / KeywordsShuffle; Mixing time; Particle systems; Cutoff; Markov chains
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