Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model. (English) Zbl 1332.60065

Summary: We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near 0. We consider both constant and variable speed models. Our estimates are sharp. As a consequence, we derive local central limit theorems, parabolic Harnack inequalities and Gaussian bounds for the heat kernel. Some of the arguments are robust and applicable for random walks on general graphs. Such results are stated under a general setting.


60G50 Sums of independent random variables; random walks
60F05 Central limit and other weak theorems
60K37 Processes in random environments
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
Full Text: DOI arXiv Euclid


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