## Journal of the Mathematical Society of Japan

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 27 October 2015

https://projecteuclid.org/euclid.jmsj/1445951155

Digital Object Identifier
doi:10.2969/jmsj/06741413

Mathematical Reviews number (MathSciNet)
MR3417502

Zentralblatt MATH identifier
1332.60065

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1445951155

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