Critical Random Walk in Random Environment on Trees of Exponential Growth

2004/04/02 by Robin Pemantle
Mathematics · #math.PR

paper · pdf

published as Proc. Sem. Stoch. Pro. 1992, Burdzy and Bass, editors, 221 - 240 (1993) · 19 pages

arxiv created 2004/04/02 · arxiv updated 2009/12/01

Abstract

This paper studies the behavior of RWRE on trees in the critical case left open in previous work. For trees of exponential growth, a random perturbation of the transition probabilities can change a transient random walk into a recurrent one. This is the opposite of what occurs on trees of sub-exponential growth.

Related

• Critical RWRE on trees and tree-indexed random walks
• Random Walk in a Random Environment and First-Passage Percolation on Trees
• A phase transition for the biased tree-builder random walk
• Renewal structure of the Tree Builder Random Walk
• A subdiffusive behaviour of recurrent random walk in random environment on a regular tree