Rate functions for random walks on random conductance models and related topics

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.

Laws of the Iterated Logarithm for random walks on Random Conductance Models

“…Remark 1.5. In this paper, we only consider discrete time Markov chains, but similar results hold for continuous time Markov chains (constant speed random walks and variable speed random walks); see [19].…”

“…We note that among the examples mentioned at the beginning of this paper, (b), (c) and (e) are for continuous time Markov chains, so the LILs will be discussed in [19].…”