%0 Journal Article
%T Martingale defocusing and transience of a self-interacting random walk
%A Yuval Peres
%A Bruno Schapira
%A Perla Sousi
%J Mathematics
%D 2014
%I arXiv
%X Suppose that $(X,Y,Z)$ is a random walk in $\mathbb{Z}^3$ that moves in the following way: on the first visit to a vertex only $Z$ changes by $\pm 1$ equally likely, while on later visits to the same vertex $(X,Y)$ performs a two-dimensional random walk step. We show that this walk is transient thus answering a question of Benjamini, Kozma and Schapira. One important ingredient of the proof is a dispersion result for martingales.
%U http://arxiv.org/abs/1403.1571v1