Continued fraction methods for random walks on ℕ and on trees

Abstract

where O < r ~ I and a is a nonnegative integer (e.g. [2], [11]). Now the Cayley-graph of a free group F s with s generators is a homogeneous tree of degree s (s edges through each vertex) and so random walks on free groups can be considered as random walks on homogeneous trees. Therefore it seems natural to study random walks on more general trees (or even graphs); this will be done in this paper. In a random walk on a graph a (one-step) transition occurs I from one vertex v to an adjacent vertex with probability d---~' where d(v) is the degree of v (uniform distribution at every vertex). We will be mainly interested in the following quantities: Let 0 be a vertex and