Asymptotic theory for the multidimensional random on-line nearest-neighbour graph
| dc.creator | Wade, Andrew R. | |
| dc.date | 2007-02-14 | |
| dc.date | 2008-09-10 | |
| dc.date.accessioned | 2026-07-07T13:12:22Z | |
| dc.date.available | 2026-07-07T13:12:22Z | |
| dc.description | The on-line nearest-neighbour graph on a sequence of $n$ uniform random points in $(0,1)^d$ ($d \in \N$) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this graph, with weight exponent $α\in (0,d/2]$, we prove $O(\max \{n^{1-(2α/d)}, \log n \})$ upper bounds on the variance. On the other hand, we give an $n \to \infty$ large-sample convergence result for the total power-weighted edge-length when $α> d/2$. We prove corresponding results when the underlying point set is a Poisson process of intensity $n$. | |
| dc.description | 25 pages; v2: substantial revision, change in title, central limit theorem present in v1 removed due to a gap | |
| dc.identifier | https://arxiv.org/abs/math/0702414 | |
| dc.identifier | http://arxiv.org/abs/math/0702414 | |
| dc.identifier | Stochastic Processes and their Applications, Vol. 119 (2009), no. 6, p. 1889-1911 | |
| dc.identifier | doi:10.1016/j.spa.2008.09.006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229558 | |
| dc.subject | Probability | |
| dc.subject | 60D05 (Primary) 60F25, 90B15, 05C80 (Secondary) | |
| dc.title | Asymptotic theory for the multidimensional random on-line nearest-neighbour graph | |
| dc.type | text |