A Law of Iterated Logarithm on Lamplighter Diagonal Products

Abstract

We prove a Law of Iterated Logarithm for random walks on a family of diagonal products constructed by Brieussel and Zheng [2]. This provides a wide variety of new examples of Law of Iterated Logarithm behaviours for random walks on groups. In particular, it follows that for any 1 2 ≤ β ≤ 1 there is a group G and random walk