๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

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

โœ Scribed by Motoko Kotani; Tomoyuki Shirai; Toshikazu Sunada

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
522 KB
Volume
159
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 probability p(n, x, y) that a particle starting at x reaches y at time n as n goes to infinity is established.

๐Ÿ“œ SIMILAR VOLUMES

An upper bound on the length of a Hamilt
An upper bound on the length of a Hamiltonian walk of a maximal planar graph
โœ Takao Asano; Takao Nishizeki; Takahiro Watanabe ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 840 KB

## Abstract A Hamiltonian walk of a connected graph is a shortest closed walk that passes through every vertex at least once, and the length of a Hamiltonian walk is the total number of edges traversed by the walk. We show that every maximal planar graph with __p__(โ‰ฅ 3) vertices has a Hamiltonian c