We prove the hydrostatics of boundary driven gradient exclusion processes, Fick's law and we present a simple proof of the dynamical large deviations principle which holds in any dimension.

We study a one-dimensional nearest neighbor simple exclusion process for which the rates of jump are chosen randomly at time zero and fixed for the rest of the evolution. The ith particle's right and left jump rates are denoted pi and qi respectively; pi+ qi = 1. We fix c [epsilon] (1/2, 1) and...

We prove an upper and a lower bound, which coincide for smooth profiles, of large deviations from the hydrodynamical limit of the empirical measure for a class of zero range processes in infinite volume starting from equilibrium. This result relies on a superexponential estimate in infinite...

We present a simple proof of a result of De Masi, Presutti, Spohn and Wick on equilibrium fluctuations of exclusion processes with speed change. The proof is based on a super-exponential inequality for fluctuation fields. It applies to gradient systems reversible with respect to product measures.

We prove a central limit theorem for the density field for stationary zero range processes in a random environment. We prove that the density field converges weakly to a generalized Ornstein-Uhlenbeck process whose evolution is described by the linearization of the hydrodynamic equation around a...

We prove the metastable behavior of reversible Markov processes on finite state spaces under minimal conditions on the jump rates. To illustrate the result we deduce the metastable behavior of the Ising model with a small magnetic field at very low temperature.