### 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 |
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Pages (from-to) | 664-689 |

Number of pages | 26 |

Journal | Journal of Functional Analysis |

Volume | 159 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 10 1998 |

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### All Science Journal Classification (ASJC) codes

- Analysis

### Cite this

*Journal of Functional Analysis*,

*159*(2), 664-689. https://doi.org/10.1006/jfan.1998.3322

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

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 159, no. 2, pp. 664-689. https://doi.org/10.1006/jfan.1998.3322

}

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.

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 -