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

Itai Benjamini, David Revelle

Research output: Contribution to journalArticlepeer-review

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 recurrent with respect to ν but transient with respect to μ. We give a number of examples of groups that have the Liouville property but have both types of instabilities. Previously known groups with these instabilities did not have the Liouville property.

Original languageEnglish
Pages (from-to)199-206
Number of pages8
JournalPotential Analysis
Volume34
Issue number2
DOIs
StatePublished - Feb 2011

All Science Journal Classification (ASJC) codes

  • Analysis

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