Scaling limits for gradient systems in random environment

Abstract

It is well known that the hydrodynamic limit of an interacting particle system satisfying a gradient condition (such as the zero-range process or the symmetric simple exclusion process) is given by a possibly non-linear parabolic equation and the equilibrium fluctuations from this limit are given by a generalized Ornstein-Uhlenbeck process. We prove that in the presence of a symmetric random environment, these scaling limits also hold for almost every choice of the random environment, with an homogenized diffusion coeficient that does not depend on the realization of the random environment.