Convergence to the maximal invariant measure for a zero-range process with random rates

E. D. Andjel, P. A. Ferrari, H. Guiol and Landim *, C.

Stochastic Processes and their Applications, 2000, vol. 90, issue 1, 67-81

Abstract: We consider a one-dimensional totally asymmetric nearest-neighbor zero-range process with site-dependent jump-rates - an 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 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.

Keywords: Zero-range; Random; rates; Invariant; measures; Convergence; to; the; maximal; invariant; measure (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (3)

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