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May 2019 Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling
Cyril Labbé, Hubert Lacoin
Ann. Probab. 47(3): 1541-1586 (May 2019). DOI: 10.1214/18-AOP1290

Abstract

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.

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Cyril Labbé. Hubert Lacoin. "Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling." Ann. Probab. 47 (3) 1541 - 1586, May 2019. https://doi.org/10.1214/18-AOP1290

Information

Received: 1 November 2016; Revised: 1 May 2018; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067276
MathSciNet: MR3945753
Digital Object Identifier: 10.1214/18-AOP1290

Subjects:
Primary: 60J27
Secondary: 37A25, 82C22

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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