Rate functions for random walks on Random conuctance Models and related topics

TL;DR

This paper investigates the laws of the iterated logarithm and rate functions for random walks in random conductance models, assuming sub-Gaussian heat kernel estimates, to understand their long-term behavior.

Contribution

It provides new insights into the asymptotic behavior of random walks on random conductance models under specific heat kernel conditions.

Findings

Establishment of laws of the iterated logarithm for these random walks

Derivation of rate functions for sample path deviations

Analysis under sub-Gaussian heat kernel estimates

Abstract

We consider laws of the iterated logarithm and the rate function for sample paths of random walks on random conductance models under the assumption that the random walks enjoy long time sub-Gaussian heat kernel estimates.