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

Motoko Kotani; Tomoyuki Shirai; Toshikazu Sunada

doi:10.1006/jfan.1998.3322

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

Motoko Kotani, Tomoyuki Shirai, Toshikazu Sunada

Research output: Contribution to journal › Article › peer-review

26 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 language	English
Pages (from-to)	664-689
Number of pages	26
Journal	Journal of Functional Analysis
Volume	159
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1998.3322
Publication status	Published - 1998 Nov 10
Externally published	Yes

Keywords

Discrete Laplacian
Discrete spectral geometry
Random walk
Transition probability

ASJC Scopus subject areas

Analysis

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10.1006/jfan.1998.3322

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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.",

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AU - Sunada, Toshikazu

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AB - 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.

KW - Discrete Laplacian

KW - Discrete spectral geometry

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KW - Transition probability

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

Abstract

Keywords

ASJC Scopus subject areas

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