Occupation Time Large Deviations for the Symmetric Simple Exclusion Process

Abstract

We obtain the decay rate of the large deviation probabilities of occupation time for the symmetric simple exclusion process. Furthermore, in dimension $d \neq 2$, we prove a large deviation principle for the occupation time. To obtain these results, we prove hydrodynamical limits for the weakly asymmetric simple exclusion process and we prove a large deviation principle for the empirical density for the symmetric simple exclusion process.