Instability of set recurrence and Green's function on groups with the Liouville property
| dc.creator | Benjamini, Itai | |
| dc.creator | Revelle, David | |
| dc.date | 2003-10-17 | |
| dc.date.accessioned | 2026-07-07T05:01:59Z | |
| dc.date.available | 2026-07-07T05:01:59Z | |
| dc.description | Let $μ$ 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.identifier | https://arxiv.org/abs/math/0310258 | |
| dc.identifier | http://arxiv.org/abs/math/0310258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68886 | |
| dc.subject | Probability | |
| dc.subject | Group Theory | |
| dc.title | Instability of set recurrence and Green's function on groups with the Liouville property | |
| dc.type | text |