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

2013/07/12 by Athreya, Siva, Bandyopadhyay, Antar, Dasgupta, Amites
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1307.3353

Abstract

We consider the random walk in an i.i.d. random environment on the infinite d-regular tree for d ≥ 3. We consider the tree as a Cayley graph of free product of finitely many copies of \Zbold and \Zbold₂ 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.

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