Mixing time and cutoff for one dimensional particle systems

Hubert Lacoin

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arXiv · 2111.06436

Mixing time and cutoff for one dimensional particle systems

Hubert Lacoin

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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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Hubert Lacoin. 2021-11-11. Mixing time and cutoff for one dimensional particle systems. https://arxiv.org/abs/2111.06436

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