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.
Citation
Sebastian Andres. Jean-Dominique Deuschel. Martin Slowik. "Invariance principle for the random conductance model in a degenerate ergodic environment." Ann. Probab. 43 (4) 1866 - 1891, July 2015. https://doi.org/10.1214/14-AOP921
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