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

We study a continuous time random walk, X, on Zd in an environment of random conductances taking values in (0,∞). 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.