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October, 2015 Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model
Omar BOUKHADRA, Takashi KUMAGAI, Pierre MATHIEU
J. Math. Soc. Japan 67(4): 1413-1448 (October, 2015). DOI: 10.2969/jmsj/06741413

Abstract

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.

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Omar BOUKHADRA. Takashi KUMAGAI. Pierre MATHIEU. "Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model." J. Math. Soc. Japan 67 (4) 1413 - 1448, October, 2015. https://doi.org/10.2969/jmsj/06741413

Information

Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1332.60065
MathSciNet: MR3417502
Digital Object Identifier: 10.2969/jmsj/06741413

Subjects:
Primary: 60G50, 60J10, 60K37

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 4 • October, 2015
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