Approximating the stationary distribution of the ASEP with open boundaries

TL;DR

This paper studies the stationary distribution of asymmetric simple exclusion processes with open boundaries, providing conditions under which the distribution approximates a product measure when projected onto growing subintervals.

Contribution

It introduces a method to approximate the stationary distribution of ASEP with open boundaries by projecting onto subintervals and characterizing when it resembles a product measure.

Findings

Stationary distribution can be approximated by a product measure under certain boundary conditions.

Projection onto growing subintervals retains key distributional properties.

Conditions depend on boundary parameters and segment size.

Abstract

We investigate the stationary distribution of asymmetric and weakly asymmetric simple exclusion processes with open boundaries. We project the stationary distribution onto a subinterval, whose size is allowed to grow with the length of the underlying segment. Depending on the boundary parameters of the exclusion process, we provide conditions such that the stationary distribution projected onto a subinterval is close in total variation distance to a product measure.