Convergence in distribution of products of random matrices: a semigroup approach

Abstract

The problem of weak convergence of the sequence of convolution powers of a probability measure has been considered in this paper in the general context of a noncompact semigroup and in particular, in the semigroup of nonnegative and real matrices. Semigroup methods have been used to give simple proofs of some recent results of Kesten and Spitzer in nonnegative matrices. It has been also shown that these methods often lead to similar results in the more general context of real matrices.