Nonequilibrium fluctuations for the occupation time of the SSEP in $d \geq 2$

TL;DR

This paper investigates the fluctuations of occupation time in the symmetric simple exclusion process in two or more dimensions, establishing invariance principles for nonequilibrium initial measures using martingale and correlation techniques.

Contribution

It provides the first invariance principles for occupation time in higher-dimensional SSEP starting from nonequilibrium states.

Findings

Proves invariance principles for occupation time in d ≥ 2

Uses martingale and correlation estimates in the proof

Extends results to nonequilibrium initial measures

Abstract

We study the symmetric simple exclusion process in two or higher dimensions. We prove the invariance principles for the occupation time when the process starts from nonequilibrium measures. Our proof combines the martingale method and correlation estimates for the exclusion process.