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VOL. 50 | 2006 Random walk on a polygon

## Abstract

A particle moves among the vertices of an $(m+1)$-gon which are labeled clockwise as $0, 1, \ldots, m$. The particle starts at $0$ and thereafter at each step it moves to the adjacent vertex, going clockwise with a known probability $p$, or counterclockwise with probability $1-p$. The directions of successive movements are independent. What is the expected number of moves needed to visit all vertices? This and other related questions are answered using recursive relations.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

Digital Object Identifier: 10.1214/074921706000000581

Subjects:
Primary: 60G50
Secondary: 60G40