A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits

Shaun McKinlay

paper

A characterisation of transient random walks on stochastic matrices with Dirichlet distributed limits

arXiv:1212.4975

Abstract

We characterise the class of distributions of random stochastic matrices $X$ with the property that the products $X (n) X (n - 1) ... X (1)$ of i.i.d. copies $X (k)$ of $X$ converge a.s. as $n \to \infty$ and the limit is Dirichlet distributed. This extends a result by Chamayou and Letac (1994) and is illustrated by several examples that are of interest in applications.