Continuum percolation with steps in an annulus
| dc.creator | Balister, Paul | |
| dc.creator | Bollobas, Bela | |
| dc.creator | Walters, Mark | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T05:18:22Z | |
| dc.date.available | 2026-07-07T05:18:22Z | |
| dc.description | Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-ε) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1 and let G_A be the random graph with vertex set {x_i} and edges x_ix_j whenever x_i-x_j\in A. We show that if the area of A is large, then G_A almost surely has an infinite component. Moreover, if we fix ε, increase r and let n_c=n_c(ε) be the area of A when this infinite component appears, then n_c\to1 as ε\to 0. This is in contrast to the case of a ``square'' annulus where we show that n_c is bounded away from 1. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051604000000891 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0503544 | |
| dc.identifier | http://arxiv.org/abs/math/0503544 | |
| dc.identifier | Annals of Applied Probability 2004, Vol. 14, No. 4, 1869-1879 | |
| dc.identifier | doi:10.1214/105051604000000891 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74638 | |
| dc.subject | Probability | |
| dc.subject | 60K35 (Primary) 82B43. (Secondary) | |
| dc.title | Continuum percolation with steps in an annulus | |
| dc.type | text |