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

Motoko Kotani, Tomoyuki Shirai, Toshikazu Sunada

Research output: Contribution to journalArticle

22 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 - Nov 10 1998

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Spectral Geometry
Transition Operator
Infinite Graphs
Transition Probability
Perturbation Theory
Asymptotic Properties
Random walk
Asymptotic Behavior
Infinity
Eigenvalue

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Asymptotic Behavior of the Transition Probability of a Random Walk on an Infinite Graph. / Kotani, Motoko; Shirai, Tomoyuki; Sunada, Toshikazu.

In: Journal of Functional Analysis, Vol. 159, No. 2, 10.11.1998, p. 664-689.

Research output: Contribution to journalArticle

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