%0 Journal Article
%T Almost sure convergence for stochastically biased random walks on trees
%A Gabriel Faraud
%A Yueyun Hu
%A Zhan Shi
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00440-011-0379-y
%X We are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assumptions, that upon the system's non-extinction, the maximal displacement of the walk in the first n steps, divided by (log n)^3, converges almost surely to a known positive constant.
%U http://arxiv.org/abs/1003.5505v5