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

Access to Document

10.1006/jfan.1998.3322

Cite this

@article{f267a7a2e7884b429fb7410cca26eefe,

title = "Asymptotic Behavior of the Transition Probability of a Random Walk on an Infinite Graph",

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.",

keywords = "Discrete Laplacian, Discrete spectral geometry, Random walk, Transition probability",

author = "Motoko Kotani and Tomoyuki Shirai and Toshikazu Sunada",

year = "1998",

month = nov,

day = "10",

doi = "10.1006/jfan.1998.3322",

language = "English",

volume = "159",

pages = "664--689",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Asymptotic Behavior of the Transition Probability of a Random Walk on an Infinite Graph

AU - Kotani, Motoko

AU - Shirai, Tomoyuki

AU - Sunada, Toshikazu

PY - 1998/11/10

Y1 - 1998/11/10

N2 - 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.

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

KW - Random walk

KW - Transition probability

UR - http://www.scopus.com/inward/record.url?scp=0000822045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000822045&partnerID=8YFLogxK

U2 - 10.1006/jfan.1998.3322

DO - 10.1006/jfan.1998.3322

M3 - Article

AN - SCOPUS:0000822045

VL - 159

SP - 664

EP - 689

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this