Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T00:48:37.252Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Cerrito, P. (1990). A complete characterization of stochastic processes defined on regular semigroups with applications to stochastic models. Illinois J. Math. 34, 108–119.Google Scholar
Clifford, A. H., and Preston, G. B. (1961). The Algebraic Theory of Semigroups. AMS, Providence, RI.Google Scholar
Hognas, G. (1977). Random semigroup acts on a finite set. Austral. Math. Soc. A 23, 481–498.Google Scholar
Hognas, G. (1979a). On random walks with continuous components. Semigroup Forum 17, 75–93.Google Scholar
Hognas, G. (1979b). On recurrent random walks on abelian semigroups. Proc. Amer. Math. Soc. 75, pp. 111–113.CrossRefGoogle Scholar
Howie, J. (1976). An Introduction to Semigroup Theory. Academic Press, New York.Google Scholar
Lallement, G. (1967). Demi-groupes réguliers. Ann. Mat. pura. appl. 77, 47–129.CrossRefGoogle Scholar
Martin-Löf, A. (1965). Probability theory on discrete semigroups. Z. Wahrscheinlichkeitsth. 4, 78–102.Google Scholar
Mukherjea, A. (1979). Limit theorems: stochastic matrices, ergodic Markov chains, and measures on semigroups. Prob. Anal. Rel. Topics 2, 143–202.Google Scholar
Mukherjea, A., and Tserpes, N. A. (1976). Measures on Topological Semigroups, Convolution Products and Random Walks. Springer, New York.Google Scholar
Rosenblat, M. (1969). Stationary measures for random walks on semigroups. In Semigroups, Proc. Sympos., Wayne State Univ., Detroit, Mich., 1968. Academic Press, New York, pp. 209–220.Google Scholar
Sun, T. C., Mukherjea, A., and Tserpes, N. A. (1973). On recurrent random walks on semigroups. Trans. Amer. Math. Soc. 185, 213–227.Google Scholar