In the investigation of limits of Markov chains, the presence of states which become instantaneous states in the limit may prevent the convergence of the chain in the Skorohod topology. We present in this article a weaker topology adapted to handle this situation. We use this topology to derive...

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 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.

We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an environment. For each environment p we prove that the set of all invariant measures is the convex hull of a set of product measures with geometric marginals. As a consequence...

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 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.