99-444 E.D. Andjel, P.A. Ferrari, H. Guiol, C. Landim

Convergence to the maximal invariant measure for a zero-range process with random rates. (43K, LaTeX2e) Nov 25, 99

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Abstract. We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates ---an \emph{environment}. For each environment $p$ we prove that the set of all invariant measures is the convex hull of a set of product measures with geometric marginals. As a consequence we show that for environments $p$ satisfying certain asymptotic property, there are no invariant measures concentrating on configurations with critical density bigger than $\rho^*(p)$, a critical value. If $\rho^*(p)$ is finite we say that there is phase-transition on the density. In this case we prove that if the initial configuration has asymptotic density strictly above $\rho^*(p)$, then the process converges to the maximal invariant measure.

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