Heat kernel estimates for random walks with degenerate weights
  We establish Gaussian-type upper bounds on the heat kernel for a continuous-time random walk on a graph with unbounded weights under an ergodicity assumption. For the proof we use Davies' perturbation method, where we show a maximal inequality for the perturbed heat kernel via Moser iteration. 
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
math.PR math.AP