On recurrent random walks on abelian semigroups

Abstract

We consider a random walk Z n {Z_n} on the locally compact second countable abelian semigroup S with unit e which is assumed to be a recurrent point for Z n {Z_n} . Then S is the disjoint union of a topologically simple abelian semigroup G and a null-set A of first category. Under some additional conditions G is a topological group.