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

Siva Athreya; Antar Bandyopadhyay; Amites Dasgupta

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

Probability 2014-04-30 v2

Authors: Siva Athreya , Antar Bandyopadhyay , Amites Dasgupta

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.

Keywords

random walk on graphs random walk in random environment random walks

Cite

@article{arxiv.1307.3353,
  title  = {Random Walks in I.I.D. Random Environment on Cayley Trees},
  author = {Siva Athreya and Antar Bandyopadhyay and Amites Dasgupta},
  journal= {arXiv preprint arXiv:1307.3353},
  year   = {2014}
}

Comments

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 well

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

Abstract

Keywords

Cite

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