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

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1610.07383(1).pdf (493.1Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
Card shuffling; Exclusion process; ASEP; Mixing time; Cutoff
Journal issue
Annals of Probability
Volume
47
Number
3
Publication date
2019
Article pages
1541-1586
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/18-AOP1290
URI
https://basepub.dauphine.fr/handle/123456789/19682
Collections
  • CEREMADE : Publications
Metadata
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Author
Labbé, Cyril
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lacoin, Hubert
87542 Instituto Nacional de Matemática Pura e Aplicada [IMPA]
Type
Article accepté pour publication ou publié
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.

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