Moderate deviation principles for the WASEP

TL;DR

This paper establishes moderate deviation principles for the fluctuation fields and occupation times of the weakly asymmetric simple exclusion process, providing insights into the process's probabilistic behavior under certain asymmetry constraints.

Contribution

It introduces the first moderate deviation principles for the fluctuation fields and occupation times of WASEP under stationary initial measures.

Findings

Proves moderate deviation principles for fluctuation fields.

Derives sample path moderate deviation principles for occupation times.

Analyzes the process under specific asymmetry constraints.

Abstract

We study the weakly asymmetric simple exclusion process on the integer lattice. Under suitable constraints on the strength of the weak asymmetry of the dynamics, we prove moderate deviation principles for the fluctuation fields when the process starts from stationary measures. As an application, we obtain sample path moderate deviation principles for the occupation time of the process in one dimension.