Summary. 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 $i$-th particle's right and left jump rates are denoted $p_i$ and $q_i$ respectively; $p_i+q_i=1$. We fix $c\in (1/2,1)$ and assume that $p_i\in[c,1]$ 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 $\rho\in(\rho^*,1]$, then there exists a product invariant distribution for the process as seen from a tagged particle with asymptotic density $\rho$; (b) if $\rho\in (0,\rho^*]$, 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. \vskip 5truemm \noindent {\it Keywords and phrases.} Asymmetric simple exclusion. Random rates. Law of large numbers. Hydrodynamical limit.
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