Asymptotic behaviour under iterated random linear transformations

Abstract

Let V be a finite-dimensional real vector space. We describe condi- tions for a sequence of the form {µ i ∗ν}, where µ is a probability measure on GL(V ) (µ i denotes the i-th convolution power of µ) and ν is a finite positive measure on V , to converge in distribution (in the vague topology) to the zero measure on V. The conditions depend on µ only via the closed subgroup ofGL( V ) generated by the support of µ.