Journal of the Mathematical Society of Japan

Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model


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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.

Article information

J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1413-1448.

First available in Project Euclid: 27 October 2015

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Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K37: Processes in random environments

Markov chains random walk random environments random conductances percolation


BOUKHADRA, Omar; KUMAGAI, Takashi; MATHIEU, Pierre. Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model. J. Math. Soc. Japan 67 (2015), no. 4, 1413--1448. doi:10.2969/jmsj/06741413.

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