### Abstract

For simple random walks (P^{n}_{G}) on a homogeneous graph G and (P^{n}_{L(G)}) on its line graph L(G), we obtain the relationship between the asymptotic behavior of the n-step transition probability P^{n}_{G}(x, x) and that of P^{n}_{L}(G)(x, x) as n→∞.

Original language | English |
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Pages (from-to) | 99-108 |

Number of pages | 10 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 52 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Asymptotic behavior of the transition probability of a simple random walk on a line graph.** / Shirai, Tomoyuki.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Asymptotic behavior of the transition probability of a simple random walk on a line graph

AU - Shirai, Tomoyuki

PY - 2000/1/1

Y1 - 2000/1/1

N2 - For simple random walks (PnG) on a homogeneous graph G and (PnL(G)) on its line graph L(G), we obtain the relationship between the asymptotic behavior of the n-step transition probability PnG(x, x) and that of PnL(G)(x, x) as n→∞.

AB - For simple random walks (PnG) on a homogeneous graph G and (PnL(G)) on its line graph L(G), we obtain the relationship between the asymptotic behavior of the n-step transition probability PnG(x, x) and that of PnL(G)(x, x) as n→∞.

UR - http://www.scopus.com/inward/record.url?scp=0042447022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042447022&partnerID=8YFLogxK

U2 - 10.2969/jmsj/05210099

DO - 10.2969/jmsj/05210099

M3 - Article

AN - SCOPUS:0042447022

VL - 52

SP - 99

EP - 108

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -