Institute of Mathematical Statistics Lecture Notes - Monograph Series

Random walk on a polygon

Jyotirmoy Sarka

Full-text: Open access


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.

Chapter information

Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page, eds., Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 31-43

First available in Project Euclid: 28 November 2007

Permanent link to this document

Digital Object Identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Gambler's ruin recursive relation conditional probability mathematical induction difference equation L'Hospital's rule Bayes' rule

Copyright © 2006, Institute of Mathematical Statistics


Sarka, Jyotirmoy. Random walk on a polygon. Recent Developments in Nonparametric Inference and Probability, 31--43, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000581.

Export citation