Nonequilibrium Joint Fluctuations for Current and Occupation Time in The Symmetric Exclusion Process

Abstract

We provide a full description for the joint fluctuations of current and occupation time in the one-dimensional nonequilibrium simple symmetric exclusion process, furnishing explicit formulas for the covariances of the limiting Gaussian process. The main novelties consist of a proof of the tightness of the nonequilibrium current based on new correlation estimates, refined estimates on the discrete gradient of the transition probabilities of the SSEP, and a nonequilibrium Kipnis-Varadhan Lemma based on a Fourier approach.