Quenched invariance principle for random walks with time-dependent ergodic degenerate weights

Abstract

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