Instability of set recurrence and Green's function on groups with the Liouville property

dc.creatorBenjamini, Itai
dc.creatorRevelle, David
dc.date2003-10-17
dc.date.accessioned2026-07-07T05:01:59Z
dc.date.available2026-07-07T05:01:59Z
dc.descriptionLet $μ$ and $ν$ be probability measures on a group Γand let G_μand G_νdenote Green's function with respect to μand ν. The group Γis said to admit instability of Green's function if there are symmetric, finitely supported measures $μ$ and νand a sequence \{x_n\} such that G_μ(e, x_n)/G_ν(e,x_n) \to 0, and Γadmits instability of recurrence if there is a set S that is recurrent with respect to νbut 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.
dc.identifierhttps://arxiv.org/abs/math/0310258
dc.identifierhttp://arxiv.org/abs/math/0310258
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68886
dc.subjectProbability
dc.subjectGroup Theory
dc.titleInstability of set recurrence and Green's function on groups with the Liouville property
dc.typetext

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