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

TL;DR

This paper establishes large deviation principles for an asymmetric zero range process with zero mean in random media, extending existing methods to infinite volume and random environments.

Contribution

It introduces a novel approach to large deviations for zero range processes in infinite volume with random jump rates, building on and extending previous methods.

Findings

Proves upper and lower bounds for large deviations from hydrodynamical limit.

Extends super-exponential estimates to infinite volume and random media.

Adapts classical methods to a more complex stochastic environment.

Abstract

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).