Random Walks in I.I.D. Random Environment on Cayley Trees

Abstract

We consider the random walk in an \emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of \Zbold and \Zbold_2 and define the i.i.d. environment as invariant under the action of this group. Under a mild non-degeneracy assumption we show that the walk is always transient.Comment: This version has been revised significantly to make the exposition better, some typing errors corrected and more details have been added to the proofs. Comparison with earlier literature has also been included and the reference list has been expanded. The title and the abstract have been suitably changed as wel