Large deviations for a zero mean asymmetric zero range process in random media

We consider an asymmetric zero range process in infinite volume with zero mean and random jump rates starting from equilibrium. We investigate the large deviations from the hydrodynamical limit of the empirical distribution of particles and prove an upper and a lower bound for the large deviation principle. Our main argument is based on a super-exponential estimate in infinite volume. For this we extend to our case a method developed by Kipnis & al. (1989) and Benois & al. (1995).Comment: 24 page

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.Comment: 41 pages, 7 figure

Hydrodynamic behavior of symmetric zero-range processes with random rates

We consider a nearest-neighbor symmetric zero-range process, evolving on the d-dimensional periodic lattice, with a random jump rate and investigate its hydrodynamic behavior. We prove that the empirical distribution of particles converges in probability to the weak solution of the non-linear diffusion equation. Our approach follows the method of entropy production introduced by Guo et al. (1988, Comm. Math. Phys. 118, 31-59). We adapt and generalize some results in Benjamini et al. (1996, Stochastic Process. Appl. 61, 181-204).Symmetric zero-range process Hydrodynamical limit Random environment