English

Harnack Inequalities and Local Central Limit Theorem for the Polynomial Lower Tail Random Conductance Model

Probability 2015-06-30 v3

Abstract

We prove upper bounds on the transition probabilities of random walks with i.i.d. random conductances with a polynomial lower tail near 00. 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.

Keywords

Cite

@article{arxiv.1308.1067,
  title  = {Harnack Inequalities and Local Central Limit Theorem for the Polynomial Lower Tail Random Conductance Model},
  author = {Omar Boukhadra and Takashi Kumagai and Pierre Mathieu},
  journal= {arXiv preprint arXiv:1308.1067},
  year   = {2015}
}

Comments

To appear in Journal of Math. Soc. Japan, special volume