We study the behavior of random walk in random environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ...

Let b be an integer greater than 1 and let Wε=(Wn ε;n≥ 0) be a random walk on the b-ary rooted tree Ub, starting at the root, going up (resp. down) with probability 1/2 + ε (resp. 1/2 - ε), ε ∈ (0, ...