Continuum percolation at and above the uniqueness treshold on homogeneous spaces
| dc.creator | Tykesson, Johan | |
| dc.date | 2007-11-02 | |
| dc.date | 2007-11-21 | |
| dc.date.accessioned | 2026-07-07T08:43:53Z | |
| dc.date.available | 2026-07-07T08:43:53Z | |
| dc.description | We consider the Poisson Boolean model of continuum percolation on a homogeneous Riemannian manifold $M$. Let $lambda$ be intensity of the Poisson process in the model and let $lambda_u$ be the infimum of the set of intensities that a.s. produce a unique unbounded component. We show that above $λ_u$ there is a.s. a unique unbounded component. We also study what happens at $λ_u$ for some spaces. In particular, if $M$ is the product of the hyperbolic disc and the real line, then at $λ_u$ there is a.s. not a unique unbounded component. The results are inspired by results for Bernoulli bond percolation on graphs due to Haggstrom, Peres and Schonmann. | |
| dc.description | 16 pages, corrections made | |
| dc.identifier | https://arxiv.org/abs/0711.0307 | |
| dc.identifier | http://arxiv.org/abs/0711.0307 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142474 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B43 | |
| dc.title | Continuum percolation at and above the uniqueness treshold on homogeneous spaces | |
| dc.type | text |