Random walks in random environments on metric groups

Random walks in random environments on countable metric groups with bounded jumps of the walking particle are considered. The transition probabilities of such a random walk from a point x is an element of G (where G is the group in question) are described by a Vector p(x) is an element of R-/W/ (where W subset of G is fixed and /W/ < infinity). The set {p(x),x is an element of G} is assumed to consist of independent identically distributed random vectors. A sufficient condition for this random walk to be transient is found. As an example, the groups Z(d), free groups, and the free product of finitely many cyclic groups of second order are considered.