Asymmetric conservative processes with random rates

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 p(i) and q(i) respectively; p(i) + q(i) = 1. We fix c is an element of (1/2, 1) and assume that rho(i) is an element of [c, 1] is a stationary ergodic process. We show that there exists a critical density rho* depending only on the distribution of {p(i)} such that for almost all choices of the rates: (a) if rho is an element of [rho*, 1], then there exists a product invariant distribution for the process as seen from a tagged particle with asymptotic density rho; (b) if rho is an element of [0, rho*), then there are no product measures invariant for the process. We give a necessary and sufficient condition for rho* > 0 in the iid case. We also show that under a product invariant distribution, the position X(t) of the tagged particle at time t can be sharply approximated by a Poisson process. Finally, we prove the hydrodynamical limit for zero range processes with random rate jumps.