Invariant Percolation and Harmonic Dirichlet Functions
| dc.creator | Gaboriau, Damien | |
| dc.date | 2004-05-24 | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:08:32Z | |
| dc.date.available | 2026-07-07T05:08:32Z | |
| dc.description | The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters in the uniqueness phase of Bernoulli percolation. We extend the result to more general invariant percolations, including the Random-Cluster model. We prove the existence of the nonuniqueness phase for the Bernoulli percolation (and make some progress for Random-Cluster model) on unimodular transitive locally finite graphs admitting nonconstant harmonic Dirichlet functions. This is done by using the device of $\ell^2$ Betti numbers. | |
| dc.description | to appear in Geometric And Functional Analysis (GAFA) | |
| dc.identifier | https://arxiv.org/abs/math/0405458 | |
| dc.identifier | http://arxiv.org/abs/math/0405458 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71301 | |
| dc.subject | Probability | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.subject | MSC: 60K35, 82B43, 31C05, 37A20, 05C25, 05C80, 37R30 | |
| dc.title | Invariant Percolation and Harmonic Dirichlet Functions | |
| dc.type | text |