Invariance Principle for the Random Conductance Model with dynamic bounded Conductances

TL;DR

This paper proves a quenched invariance principle for a continuous-time random walk in a dynamic environment with bounded conductances, establishing fundamental limit behaviors and connecting to stochastic interface models.

Contribution

It introduces a quenched invariance principle for the model with dynamic conductances, extending previous static results to a more general setting.

Findings

Proved a quenched invariance principle for the model.

Established Green's function bounds and a local limit theorem.

Connected the model to stochastic interface models.

Abstract

We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X, and obtain Green's functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.