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Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling

Labbé, Cyril; Lacoin, Hubert (2019), Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling, Annals of Probability, 47, 3, p. 1541-1586. 10.1214/18-AOP1290

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Annals of Probability
Volume
47
Number
3
Publisher
Institute of Mathematical Statistics
Pages
1541-1586
Publication identifier
Metadata
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Author(s)
Labbé, Cyril
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lacoin, Hubert
Instituto Nacional de Matemática Pura e Aplicada [IMPA]
Abstract (EN)
We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times, thus showing that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunction, stochastic comparisons and concentration inequalities.
Subjects / Keywords
Card shuffling; Exclusion process; ASEP; Mixing time; Cutoff