Excited Random Walk on Trees

Abstract

We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $1-\varepsilon$ when it visits a vertex for the first time. At all other times it behaves like a simple random walk on $G$. We show that for all $\varepsilon\ge 0$ this process is transient. Also we consider a generalization of this process and establish its transience in some cases.