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

TL;DR

This paper proves a quenched invariance principle for a continuous-time random walk in a dynamic, ergodic environment with degenerate weights, using Moser's iteration to handle sublinearity of the corrector.

Contribution

It establishes a quenched invariance principle for random walks with time-dependent ergodic degenerate weights, advancing understanding of such stochastic processes.

Findings

Proves quenched invariance principle under moment conditions.

Employs Moser's iteration for sublinearity of the corrector.

Handles environments with degenerate, time-dependent conductances.

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.