The Annals of Probability

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

Cyril Labbé and Hubert Lacoin

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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.

Article information

Ann. Probab., Volume 47, Number 3 (2019), 1541-1586.

Received: November 2016
Revised: May 2018
First available in Project Euclid: 2 May 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 37A25: Ergodicity, mixing, rates of mixing 82C22: Interacting particle systems [See also 60K35]

Card shuffling exclusion process ASEP mixing time cutoff


Labbé, Cyril; Lacoin, Hubert. Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling. Ann. Probab. 47 (2019), no. 3, 1541--1586. doi:10.1214/18-AOP1290.

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