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
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
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
VL - 159
SP - 664
EP - 689
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -