Joint work with Jacoboni and Lorensen

Abstract: Random walks on the Cayley graph of a soluble group are of interest
because soluble groups are amenable and therefore by Keston’s characterization of
amenability their return probabilities perform more strongly than exponential decay.
In this talk we examine some work of Jacoboni on how structure of soluble groups influences
the progress of random walks. The study of soluble groups with no large wreath product sections
naturally belongs to this context and we describe new joint work with Jacoboni giving
structural information about such groups. The interaction with amenability can be further
investigated using new results of Bartholdi and Kielak and giving rise to a new 
characterisation of amenability in terms of finiteness properties of group algebras.