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Labbé, Cyril; Lacoin, Hubert

Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling. (English) Zbl 1466.60152

Ann. Probab. 47, No. 3, 1541-1586 (2019).
Summary: We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our results show 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 eigenfunctions, stochastic comparisons and concentration inequalities.

Cited in 1 Review
Cited in 35 Documents

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
37A25 Ergodicity, mixing, rates of mixing
82C22 Interacting particle systems in time-dependent statistical mechanics

Keywords:

card shuffling; exclusion process; ASEP; mixing time; cutoff
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References:

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