Slow movement of random walk in random environment on a regular tree

Yueyun Hu, Zhan Shi

Published 2006-08-01Version 1

We consider a recurrent random walk in random environment on a regular tree. Under suitable general assumptions upon the distribution of the environment, we show that the walk exhibits an unusual slow movement: the order of magnitude of the walk in the first $n$ steps is $(\log n)^3$.