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

Omar Boukhadra, Takashi Kumagai, Pierre Mathieu

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1413-1448
Number of pages36
JournalJournal of the Mathematical Society of Japan
Volume67
Issue number4
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Markov chains
  • Percolation
  • Random conductances
  • Random environments
  • Random walk

ASJC Scopus subject areas

  • Mathematics(all)

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