Mixing times for the open ASEP at the triple point

TL;DR

This paper analyzes the mixing times of the open ASEP at the triple point, revealing how they scale with system size and bias parameter, using advanced probabilistic techniques and couplings.

Contribution

It provides new precise estimates of mixing times for the open ASEP at the triple point, including scaling laws and bounds in different density phases.

Findings

Mixing time scales as N^{3/2+κ} for certain bias parameters.

Poly-logarithmic corrections appear at κ=1/2.

Comparison between moderate deviations in open ASEP and ASEP on integers.

Abstract

We consider mixing times for the open asymmetric simple exclusion process (ASEP) at the triple point. We show that the mixing time of the open ASEP on a segment of length $N$ for bias parameter $q$ is of order $N^{3/2+\kappa}$ if $1-q \asymp N^{-\kappa}$ for some $\kappa \in [0,\frac{1}{2})$, and the same result with poly-logarithmic corrections for $\kappa=\frac{1}{2}$. Our proof combines a fine analysis of the current of the open ASEP, moderate deviations of second class particles, the censoring inequality, and various couplings and multi-species extensions of the ASEP. Moreover, we establish a comparison between moderate deviations for the current of the open ASEP and the ASEP on the integers, as well as bounds on mixing times for the open ASEP in the weakly high density phase, which are of independent interest.