Instability of Set Recurrence and Green’s Function on Groups with the Liouville Property

Abstract

Let μ and ν be probability measures on a group Γ and let Gμ and Gν denote Green’s function with respect to μ and ν. The group Γ is said to admit instability of Green’s function if there are symmetric, finitely supported measures μ and ν and a sequence {xn} such that Gμ(e, xn)/Gν(e, xn) → 0, and Γ admits instability of recurrence if there is a set S that is… (More)

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