Random semigroup acts on a finite set
1977 ◽
Vol 23
(4)
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pp. 481-498
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AbstractLet 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.