Limit theory for the random on-line nearest-neighbour graph
| dc.creator | Penrose, Mathew D. | |
| dc.creator | Wade, Andrew R. | |
| dc.date | 2006-03-23 | |
| dc.date.accessioned | 2026-07-07T09:38:05Z | |
| dc.date.available | 2026-07-07T09:38:05Z | |
| dc.description | In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic behaviour of the total power-weighted length of the ONG on uniform random points in (0,1)^d. In particular, for d=1 and weight exponent α>1/2, the limiting distribution of the centred total weight is characterized by a distributional fixed-point equation. As an ancillary result, we give exact expressions for the expectation and variance of the standard nearest-neighbour (directed) graph on uniform random points in the unit interval. | |
| dc.description | 28 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0603561 | |
| dc.identifier | http://arxiv.org/abs/math/0603561 | |
| dc.identifier | Random Structures and Algorithms, Vol. 32 (2008), no. 2, p. 125-156 | |
| dc.identifier | doi:10.1002/rsa.20185 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160681 | |
| dc.subject | Probability | |
| dc.subject | 60D05, 60F05 (Primary) 90B15 (Secondary) | |
| dc.title | Limit theory for the random on-line nearest-neighbour graph | |
| dc.type | text |