Rate of Escape on the Lamplighter Tree
Abstract
Description
Suppose we are given a homogeneous tree $\mathcal{T}_q$ of degree $q\geq 3$, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product $(\mathbb{Z}/2)\wr Γ$, where $Γ=\ast_{i=1}^q \mathbb{Z}/2$ is the free product group of $q$ factors $\mathbb{Z}/2$. We consider a transient random walk on a Cayley graph of $(\mathbb{Z}/2)\wr Γ$, for which we want to compute lower and upper bounds for the rate of escape, that is, the speed at which the random walk flees to infinity.
16 pages; accepted for publication in Journal of Mathematical Sciences (N.Y.)
16 pages; accepted for publication in Journal of Mathematical Sciences (N.Y.)