The open ASEP with light particles

TL;DR

This paper analyzes the stationary distribution and mixing times of the open ASEP with light particles, providing new insights into particle locations, densities, and phase behavior using advanced mathematical tools.

Contribution

It introduces new results on the asymptotic locations of light particles and mixing times in open ASEP, employing matrix product ansatz and deviation techniques.

Findings

Asymptotic locations of light particles characterized.

Mixing times in high and low density phases studied.

Particle densities at single sites derived for standard ASEP.

Abstract

We consider the stationary measure of the open asymmetric simple exclusion process (ASEP) with light particles. We prove several results on the asymptotic locations of the light particles under the stationary measure. Moreover, in the fan region of the high and low density phases, we study the mixing times for open ASEP with light particles. Our approach involves the matrix product ansatz, Askey-Wilson signed measures, moderate deviation results for second class particles, as well as various coupling arguments. Along the way we obtain the particle densities at single sites for the standard open ASEP without light particles, which are of independent interest.