Random walk on a polygon

Details Random walk on a polygon Random walk on a polygon

2006-11-22

arxiv.org/abs/math/0611676v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 31-43

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000581 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000581

A particle moves among the vertices of an $(m+1)$-gon which are labeled clockwise as $0,1,...,m$. 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.

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