Nonequilibrium fluctuations and moderate deviations for the occupation time of the SSEP with Glauber dynamics

TL;DR

This paper investigates the occupation time fluctuations of the symmetric simple exclusion process with Glauber dynamics, establishing central limit theorems and moderate deviation principles in different dimensions.

Contribution

It provides new fluctuation and deviation results for the SSEP with Glauber dynamics starting from nonequilibrium measures, using martingale and entropy methods.

Findings

Proves CLTs for occupation time in 2D

Establishes moderate deviation principles in 1D

Relates occupation time to density fluctuations via logarithmic Sobolev inequality

Abstract

We study the symmetric simple exclusion process with Glauber dynamics. When the process starts from a nonequilibrium measure, we prove central limit theorems for the occupation time in dimension two, and sample path moderate deviation principles in dimension one. For the fluctuations, we use the martingale method and the sharp relative entropy method from [Jara and Menezes, arXiv:1810.09526]. For the moderate deviations, the main idea is to relate the occupation time to the density fluctuation field by using the logarithmic Sobolev inequality from the Glauber dynamics.