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Random walks on finite semigroups

Part of: Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

George R. Barnes ,
Patricia B. Cerrito  and
Inessa Levi
George R. Barnes*
Affiliation:
University of Louisville
Patricia B. Cerrito*
Affiliation:
University of Louisville
Inessa Levi*
Affiliation:
University of Louisville
*
∗ Postal address: Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
∗ Postal address: Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
∗ Postal address: Department of Mathematics, University of Louisville, Louisville, KY 40292, USA
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Abstract

The purpose of this paper is to study the asymptotic properties of Markov chains on semigroups. In particular, the structure of transition matrices representing random walks on finite semigroups is examined. It is shown that the transition matrices associated with certain semigroups are block diagonal with identical blocks. The form of the blocks is determined via the algebraic structure of the semigroup.

Keywords

Random walkprobability transition matrixsemigroupGreen's relations

MSC classification

Primary: 60B05: Probability measures on topological spaces 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 824 - 832
Copyright
Copyright © Applied Probability Trust 1998 

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