Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius
| dc.creator | Calka, Pierre | |
| dc.creator | Schreiber, Tomasz | |
| dc.date | 2005-07-22 | |
| dc.date.accessioned | 2026-07-07T05:21:55Z | |
| dc.date.available | 2026-07-07T05:21:55Z | |
| dc.description | In this paper, we are interested in the behavior of the typical Poisson-Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to infinity. We prove a law of large numbers for its number of vertices and the area of the cell outside the disk. Moreover, for the latter, we establish a central limit theorem as well as moderate deviation type results. The proofs deeply rely on precise connections between Poisson-Voronoi tessellations, convex hulls of Poisson samples and germ-grain models in the unit ball. Besides, we derive analogous facts for the Crofton cell of a stationary Poisson line process in the plane. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000134 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0507463 | |
| dc.identifier | http://arxiv.org/abs/math/0507463 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 4, 1625-1642 | |
| dc.identifier | doi:10.1214/009117905000000134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75867 | |
| dc.subject | Probability | |
| dc.subject | 60D05, 60F10 (Primary) 60G55 (Secondary) | |
| dc.title | Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius | |
| dc.type | text |