Limits of convolution iterates and properties of random walks defined on regular semigroups with applications to matrix semigroups

Abstract

We consider the properties of a random walk Z n = X 1 X 2 … defined on a topological semigroup S which has the additional property that every element of S has a generalized inverse. We give conditions for when Z n is recurrent and also consider the value of α = sup K ⊂ S, K compact lim n → ∞ sup x ϵ S μ n ( Kx −1). Since every matrix has at least one generalized inverse, the techniques presented will be applied to semigroups of matrices.