 99444 E.D. Andjel, P.A. Ferrari, H. Guiol, C. Landim
 Convergence to the maximal invariant measure
for a zerorange process with random rates.
(43K, LaTeX2e)
Nov 25, 99

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Abstract. We consider a onedimensional totally asymmetric
nearestneighbor zerorange process with sitedependent jumprates
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
phasetransition 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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