Asymptotic Behavior of the Transition Probability of a Random Walk on an Infinite Graph

Motoko Kotani, Tomoyuki Shirai, Toshikazu Sunada

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

Ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition. In the course of our argument, we employ perturbation theory for the maximal eigenvalues of twisted transition operator. As a result, an asymptotic of the probabilityp(n,x,y) that a particle starting atxreachesyat timenasngoes to infinity is established.

Original languageEnglish
Pages (from-to)664-689
Number of pages26
JournalJournal of Functional Analysis
Volume159
Issue number2
DOIs
Publication statusPublished - 1998 Nov 10
Externally publishedYes

Keywords

  • Discrete Laplacian
  • Discrete spectral geometry
  • Random walk
  • Transition probability

ASJC Scopus subject areas

  • Analysis

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