Invariance principle for the random conductance model in a degenerate ergodic environment

Abstract

We study a continuous time random walk, $X$, on $\mathbb{Z}^{d}$ in an environment of random conductances taking values in $(0,\infty)$. We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for $X$ under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.