Institute of Mathematical Statistics Lecture Notes - Monograph Series
Random walk on a polygon
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.
First available in Project Euclid: 28 November 2007
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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. https://projecteuclid.org/euclid.lnms/1196284051