@article{EJP591,
author = {Alessandra Faggionato},
title = {Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {disordered system; bond percolation; random walk in random environment; exclusion process; homogenization},
abstract = {We consider a stationary and ergodic random field $\{\omega (b):b \in \mathbb{E}_d \}$ parameterized by the family of bonds in $\mathbb{Z}^d$, $d\geq 2$. The random variable $\omega(b)$ 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 $\mathcal{C}(\omega)$, we prove homogenization results for the random walk among random conductances on $\mathcal{C}(\omega)$. As a byproduct, applying the general criterion of Faggionato (2007) 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 $\mathcal{C}(\omega)$. 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, $\mathcal{C}(\omega)$ can be the infinite cluster of supercritical Bernoulli bond percolation.},
pages = {no. 73, 2217-2247},
issn = {1083-6489},
doi = {10.1214/EJP.v13-591},
url = {http://ejp.ejpecp.org/article/view/591}}