Invariance principle for the random conductance model with unbounded conductances

TL;DR

This paper establishes heat kernel bounds and a quenched invariance principle for a continuous-time random walk in an environment with i.i.d. conductances that are unbounded, including cases where the expected conductance is infinite.

Contribution

It extends invariance principles and heat kernel estimates to models with unbounded conductances, even when the mean conductance is infinite.

Findings

Proved heat kernel bounds for the model.

Established quenched invariance principle under unbounded conductances.

Demonstrated results hold without finite mean of conductances.

Abstract

We study a continuous time random walk $X$ in an environment of i.i.d. random conductances $\mu_e\in[1,\infty)$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when ${\mathbb{E}}\mu_e=\infty$.