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

By S. Andres, Alberto Chiarini, Jean-Dominique Deuschel, Martin Slowik. 2016

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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.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0d065d10d4150fb8608e594769596581e1554185