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
