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Random walks on trees

✍ Scribed by Lynn Hauser Pearce

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 267 KB
Volume: 30
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90234-4

No coin nor oath required. For personal study only.

✦ Synopsis

The classical gambler's ruin problem, i.e., a random walk along a line may be viewed q raph theoretically as a random walk along a path with the endpoints as absorbing states. This paper is an i0vestigation of the natural generalization of this problem to that of a particle walking randomly on a tree with the endpoints as absorbing barriers. Expressions i. terms of the graph structure are t,btained for the probability of absorption at an endpoint e in a walk originating from a vertex v. as well as for the expected length of a walk.

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