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

Cyril Labbé (1, 2) , Hubert Lacoin (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 IMPA-Brazil

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.

Domaines: Probabilités [math.PR]

Cyril Labbé, Hubert Lacoin. Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling. Annals of Probability, 2019, ⟨10.1214/18-AOP1290⟩. ⟨hal-01428017⟩