95-42 I. Benjamini, P. A. Ferrari, C. Landim

Asymmetric conservative processes with random rates (69K, TeX) Feb 6, 95

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 95-42.tex