Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances

[摘要] We establish heat kernel upper bounds for a continuous-time random walk under unbounded conductances satisfying an integrability assumption, where we correct and extend recent results in [3] to a general class of speed measures. The resulting heat kernel estimates are governed by the intrinsic metric induced by the speed measure. We also provide a comparison result of this metric with the usual graph distance, which is optimal in the context of the random conductance model with ergodic conductances.

[学科分类] 统计和概率

[关键词] random walk;heat kernel;intrinsic metric