Wade, A.R. (2009) Asymptotic theory for the multidimensional random on-line nearest-neighbour graph. Stochastic Processes and their Applications, 119. pp. 1889-1911. ISSN 0304-4149
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Official URL: http://dx.doi.org/10.1016/j.spa.2008.09.006
Abstract
The on-line nearest-neighbour graph on a sequence of n uniform random points in (0,1)d 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 αset membership, variant(0,d/2], we prove O(max{n1−(2α/d),logn}) upper bounds on the variance. On the other hand, we give an n→∞ 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.
| Item type: | Article |
|---|---|
| ID code: | 13393 |
| Keywords: | random spatial graphs, network evolution, variance asymptotics, martingale dierences, statistics, Probabilities. Mathematical statistics, Mathematics |
| Subjects: | Science > Mathematics > Probabilities. Mathematical statistics Science > Mathematics |
| Department: | Faculty of Science > Mathematics and Statistics |
| Related URLs: | |
| Depositing user: | Mrs Carolynne Westwood |
| Date Deposited: | 12 Nov 2009 14:06 |
| Last modified: | 06 Oct 2012 08:16 |
| URI: | http://strathprints.strath.ac.uk/id/eprint/13393 |
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