Mixing times for the TASEP in the maximal current phase

Dominik Schmid

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arXiv · 2104.12745

Mixing times for the TASEP in the maximal current phase

Dominik Schmid

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Abstract

We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a segment of size $N$ with open boundaries. We focus on the maximal current phase, and prove that the mixing time is of order $N^{3/2}$, up to logarithmic corrections. In the triple point, where the TASEP with open boundaries approaches the Uniform distribution on the state space, we show that the mixing time is precisely of order $N^{3/2}$. This is conjectured to be the correct order of the mixing time for a wide range of particle systems with maximal current. Our arguments rely on a connection to last-passage percolation, and recent results on moderate deviations of last-passage times.

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Dominik Schmid. 2021-04-26. Mixing times for the TASEP in the maximal current phase. https://arxiv.org/abs/2104.12745

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