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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 73 open journal systems 


Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit

Alessandra Faggionato, Department of Mathematics. University La Sapienza, Rome. Italy


Abstract
We consider a stationary and ergodic random field parameterized by the family of bonds in Z^d, d>=2. The random variable associated to the bond b is thought of as the conductance of bond b and it ranges in a finite interval [0,c_0]. Assuming that the set of bonds with positive conductance has a unique infinite cluster C, we prove homogenization results for the random walk among random conductances on C. As a byproduct, applying a general criterion developed in a previous paper and leading to the hydrodynamic limit of exclusion processes with bond-dependent transition rates, for almost all realizations of the environment we prove the hydrodynamic limit of simple exclusion processes among random conductances on C. The hydrodynamic equation is given by a heat equation whose diffusion matrix does not depend on the environment. We do not require any ellipticity condition. As special case, C can be the infinite cluster of supercritical Bernoulli bond percolation.


Full text: PDF

Pages: 2217-2247

Published on: December 21, 2008
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Electronic Journal of Probability. ISSN: 1083-6489