Moderate deviation principles for the current and the tagged particle in the WASEP

TL;DR

This paper establishes moderate deviation principles for the current and tagged particle in the one-dimensional weakly asymmetric simple exclusion process, extending previous symmetric case results.

Contribution

It provides simplified proofs for moderate deviation principles in the WASEP, advancing understanding of fluctuations in asymmetric exclusion processes.

Findings

Sample path moderate deviation principles proved for current and tagged particle.

Results extend previous symmetric exclusion process findings.

Proofs are simplified compared to earlier works.

Abstract

We study the weakly asymmetric simple exclusion process in one dimension. We prove sample path moderate deviation principles for the current and the tagged particle when the process starts from one of its stationary measures. We simplify the proof in our previous works [Xue and Zhao, Electronic Journal of Probability, 2024] and [Xue and Zhao, Stochastic Processes and their Applications, 2023], where the same problem was investigated in the symmetric simple exclusion process.