Percolating paths through random points :
| dc.creator | Aldous, David | |
| dc.creator | Krikun, Maxim | |
| dc.date | 2005-09-21 | |
| dc.date.accessioned | 2026-07-07T06:18:33Z | |
| dc.date.available | 2026-07-07T06:18:33Z | |
| dc.description | We prove consistency of four different approaches to formalizing the idea of minimum average edge-length in a path linking some infinite subset of points of a Poisson process. The approaches are (i) shortest path from origin through some $m$ distinct points; (ii) shortest average edge-length in paths across the diagonal of a large cube; (iii) shortest path through some specified proportion $δ$ of points in a large cube; (iv) translation-invariant measures on paths in $\Reals^d$ which contain a proportion $δ$ of the Poisson points. We develop basic properties of a normalized average length function $c(δ)$ and pose challenging open problem | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509492 | |
| dc.identifier | http://arxiv.org/abs/math/0509492 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94773 | |
| dc.subject | Probability | |
| dc.subject | 60K35 | |
| dc.title | Percolating paths through random points : | |
| dc.type | text |