Mixing time and cutoff for one dimensional particle systems

2021/11/11 by Lacoin, Hubert
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.06436

Abstract

We survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (symmetric and asymmetric) and a continuum analog, the simple random walk on the simplex with an emphasis on cutoff results. A Markov chain is said to exhibit cutoff if on a certain time scale, the distance to equilibrium drops abruptly from 1 to 0. We also review a couple of techniques used to obtain these results by exposing and commenting some elements of proof.

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