On heat kernel decay for the random conductance model

TL;DR

This paper investigates the decay behavior of the heat kernel for random walks in environments with i.i.d. conductances, providing improved results and techniques to understand anomalous decay patterns.

Contribution

It advances the understanding of heat kernel decay in the random conductance model by refining existing results and introducing new analytical techniques.

Findings

Enhanced bounds on heat kernel decay rates

Identification of conditions leading to anomalous decay

Development of novel analytical methods

Abstract

We study discrete time random walks in an environment of i.i.d. non-negative bounded conductances in $\mathbb{Z}^d$. We are interested in the anomaly of the heat-kernel decay. We improve recent results and techniques.