Large deviation principle for the stationary measures of open asymmetric simple exclusion processes

TL;DR

This paper rigorously proves the large deviation principle for the stationary measures of open ASEP on finite intervals, confirming predictions from physics in the fan region of the phase diagram.

Contribution

It provides the first rigorous proof of the large deviation principle for open ASEP's stationary measures in the fan region, using a two-layer measure expression and recent LDP results.

Findings

Confirmed the large deviation principle for open ASEP in the fan region.

Connected matrix product ansatz with large deviation analysis.

Validated physics-based predictions with rigorous mathematics.

Abstract

We consider the stationary measure of the asymmetric simple exclusion process (ASEP) on a finite interval in $\mathbb{Z}$ with open boundaries. Fixing all the jump rates and letting the system size approach infinity, the height profile of such a sequence of stationary measures satisfies a large deviation principle (LDP), whose rate function was predicted in the physics work arXiv:cond-mat/0205353. In this paper, we provide the first rigorous proof of the large deviation principle in the "fan region" part of the phase diagram. Our proof relies on two key ingredients: a two-layer expression of the stationary measure of open ASEP, arising from the Enaud-Derrida representation arXiv:cond-mat/0307023 of the matrix product ansatz, and the large deviation principle of the open totally asymmetric simple exclusion process (TASEP) recently established in arXiv:2403.03275.