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

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U2 - 10.1006/jfan.1998.3322

DO - 10.1006/jfan.1998.3322

M3 - Article

AN - SCOPUS:0000822045

SN - 0022-1236

VL - 159

SP - 664

EP - 689

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -