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

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.