Trees and matchings from point processes
| dc.creator | Holroyd, Alexander E. | |
| dc.creator | Peres, Yuval | |
| dc.date | 2002-11-29 | |
| dc.date.accessioned | 2026-07-07T04:53:24Z | |
| dc.date.available | 2026-07-07T04:53:24Z | |
| dc.description | A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the d-dimensional Poisson process has a one-ended tree as a factor graph. This implies that the Poisson points can be given an ordering isomorphic to the usual ordering of the integers in a deterministic isometry-invariant way. For d \geq 4 our result answers a question posed by Ferrari, Landim and Thorisson. We prove also that any isometry-invariant ergodic point process of finite intensity in Euclidean or hyperbolic space has a perfect matching as a factor graph provided all the inter-point distances are distinct. | |
| dc.identifier | https://arxiv.org/abs/math/0211455 | |
| dc.identifier | http://arxiv.org/abs/math/0211455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65832 | |
| dc.subject | Probability | |
| dc.subject | 60G55; 60K35 | |
| dc.title | Trees and matchings from point processes | |
| dc.type | text |