Explicit laws of large numbers for random nearest-neighbour type graphs
| dc.creator | Wade, Andrew R. | |
| dc.date | 2006-03-23 | |
| dc.date | 2007-02-14 | |
| dc.date.accessioned | 2026-07-07T09:38:05Z | |
| dc.date.available | 2026-07-07T09:38:05Z | |
| dc.description | Under the unifying umbrella of a general result of Penrose & Yukich [Ann. Appl. Probab., (2003) 13, 277--303] we give laws of large numbers (in the $L^p$ sense) for the total power-weighted length of several nearest-neighbour type graphs on random point sets in $\R^d$, $d\in\N$. Some of these results are known; some are new. We give limiting constants explicitly, where previously they have been evaluated in less generality or not at all. The graphs we consider include the k-nearest neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the on-line nearest-neighbour graph. | |
| dc.description | 18 pages, 2 figures; revised presentation | |
| dc.identifier | https://arxiv.org/abs/math/0603559 | |
| dc.identifier | http://arxiv.org/abs/math/0603559 | |
| dc.identifier | Advances in Applied Probability, Vol. 39 (2007), no. 2, p. 326-342 | |
| dc.identifier | doi:10.1239/aap/1183667613 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160680 | |
| dc.subject | Probability | |
| dc.subject | 60D05 (Primary) 60F25 (Secondary) | |
| dc.title | Explicit laws of large numbers for random nearest-neighbour type graphs | |
| dc.type | text |