Moduli of continuity of local times of random walks on graphs in terms of the resistance metric

Abstract

In this article, universal concentration estimates are established for the local times of random walks on weighted graphs in terms of the resistance metric. As a particular application of these, a modulus of continuity for local times is provided in the case when the graphs in question satisfy a certain volume growth condition with respect to the resistance metric. Moreover, it is explained how these results can be applied to self-similar fractals, for which they are shown to be useful for deriving scaling limits for local times and asymptotic bounds for the cover time distribution.

References in corpus (5)

• Critical random graphs: Diameter and mixing time
• Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
• The cover time, the blanket time, and the Matthews bound
• Cover times for sequences of reversible Markov chains on random graphs
• Mixing and relaxation time for Random Walk on Wreath Product Graphs

Cited by in corpus (4)

• Laws of the iterated logarithm for symmetric jump processes
• Time-changes of stochastic processes associated with resistance forms
• Convergence of blanket times for sequences of random walks on critical random graphs
• Lamplighter random walks on fractals