Heat kernel estimates for strongly recurrent random walk on random media

Takashi Kumagai*, Jun Misumi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385-431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.

Original languageEnglish
Pages (from-to)910-935
Number of pages26
JournalJournal of Theoretical Probability
Volume21
Issue number4
DOIs
Publication statusPublished - 2008 Dec
Externally publishedYes

Keywords

  • Heat kernel estimates
  • Long-range percolation
  • Random media
  • Random walk
  • Spectral dimension

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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