Nonequilibrium moderate deviations from hydrodynamics of the simple symmetric exclusion process

Abstract

In this paper, we give the moderate deviation principle from the hydrodynamic limit of the simple symmetric exclusion process on the 1-dimensional torus starting from a nonequilibrium state, which extends the result given in Gao and Quastel (2003) about the case where the process starts from an equilibrium state. The exponential tightness of the scaled density field of the process and a replacement lemma play key roles in the proof of the main result. We utilize Grownwall’s inequality and the upper bound of the large deviation principle given in Kipnis, Olla and Varadhan (1989) to prove the above exponential tightness and the replacement lemma respectively in the absence of the invariance of the initial distribution.