Contents 1. Introduction 2 2. Basic definitions and preliminaries 3 A. Adaptedness to the graph structure 4 B. Reversible Markov chains 4 C. Random walks on groups 5 D. Group-invariant random walks… (More)

This paper is devoted to the study of random walks on infinite trees with finitely many cone types (also called periodic trees). We consider nearest neighbour random walks with probabilities adapted… (More)

Let T q be the homogeneous tree with degree q + 1 ≥ 3 and G a finitely generated group whose Cayley graph is T q. The associated lamplighter group is the wreath product Z r ≀ G, where Z r is the… (More)

When does the Cayley graph of a finitely generated, infinite group look similar to a tree? For a locally finite, infinite graph, one can introduce different notions of “metric” type saying that it is… (More)

The lamplighter group over Z is the wreath product Z q ≀ Z. With respect to a natural generating set, its Cayley graph is the Diestel-Leader graph DL(q, q). We study harmonic functions for the "… (More)

Let X be a locally finite, connected graph without vertices of degree 1. Non-backtracking random walk moves at each step with equal probability to one of the “forward” neighbours of the actual state,… (More)

Let T1, . . . , Td be homogeneous trees with degrees q1 + 1, . . . , qd + 1 ≥ 3, respectively. For each tree, let h : Tj → Z be the Busemann function with respect to a fixed boundary point (end). Its… (More)