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Random semigroup acts on a finite set

Published online by Cambridge University Press:  09 April 2009

Göran Högnäs
Göran Högnäs
Affiliation:
Department of Mathematics, Åbo Akademi, Henriksgatan 9, SF-20500 Åbo 50, Finland.
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Abstract

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Let X be a finite set and S a semigroup of transformations of X. We investigate the trace on X of a random walk on S. We relate the structure of the trace process, which turns out to be a Markov chain, to that of the random walk. We show, for example, that all periods of the trace process divide the period of the random walk.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 481 - 498
Copyright
Copyright © Australian Mathematical Society 1977

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