 9542 I. Benjamini, P. A. Ferrari, C. Landim
 Asymmetric conservative processes with random rates
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Feb 6, 95

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Abstract. 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 and a (fixed) density $\rho^*< \rho \le 1$
there exists an invariant distribution for the process as seen from a
tagged particle with asymptotic density $\rho$. Under this measure, the
distribution of the distances between particles are independent random
variables. We also show that under the 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.
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