Heat kernel estimates for random walks with degenerate weights

TL;DR

This paper derives Gaussian upper bounds for the heat kernel of a continuous-time random walk on a graph with unbounded weights, using Davies' perturbation method and Moser iteration under ergodicity assumptions.

Contribution

It introduces a novel approach to estimate heat kernels for random walks with unbounded weights on graphs, extending existing methods to more general settings.

Findings

Established Gaussian upper bounds for heat kernels

Applied Davies' perturbation method with Moser iteration

Extended heat kernel estimates to graphs with unbounded weights

Abstract

We establish Gaussian-type upper bounds on the heat kernel for a continuous-time random walk on a graph with unbounded weights under an ergodicity assumption. For the proof we use Davies' perturbation method, where we show a maximal inequality for the perturbed heat kernel via Moser iteration.