## The Annals of Probability

- Ann. Probab.
- Volume 14, Number 4 (1986), 1411-1417.

### Recurrence of Random Walks on Completely Simple Semigroups

#### Abstract

A completely simple semigroup has the form $S = X \times G \times Y$. This paper considers the relationship between $S$ and $G$. Given a recurrent random walk on $S$ we determine under what conditions $G$ is also recurrent and conversely. In particular we generalize the results of Larisse.

#### Article information

**Source**

Ann. Probab., Volume 14, Number 4 (1986), 1411-1417.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176992382

**Digital Object Identifier**

doi:10.1214/aop/1176992382

**Mathematical Reviews number (MathSciNet)**

MR866362

**Zentralblatt MATH identifier**

0606.60013

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B10: Convergence of probability measures

Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

**Keywords**

Random walk topological semigroup

#### Citation

Cerrito, P. B. Recurrence of Random Walks on Completely Simple Semigroups. Ann. Probab. 14 (1986), no. 4, 1411--1417. doi:10.1214/aop/1176992382. https://projecteuclid.org/euclid.aop/1176992382