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.

34 pages; in this version a minor technical gap in the proof of the results in Section 5 has been removed

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• An almost sure invariance principle for random walks in a space-time random environment
• Random Walk in Dynamic Markovian Random Environment
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