Suppose we are given a homogeneous tree Tq of degree q ≥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product (Z/2) ∫Γ, where Γ = *q/i=1Z/2 is the free product group of q factors Z/2. We consider a transient random walk on a Cayley graph of (Z/2) ∫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.
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