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 language | English |
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Pages (from-to) | 199-206 |
Number of pages | 8 |
Journal | Potential Analysis |
Volume | 34 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2011 |
All Science Journal Classification (ASJC) codes
- Analysis