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Asymptotic theory for the multidimensional random on-line nearest-neighbour graph.

Wade, Andrew R. (2009) 'Asymptotic theory for the multidimensional random on-line nearest-neighbour graph.', Stochastic processes and their applications., 119 (6). pp. 1889-1911.

Abstract

The on-line nearest-neighbour graph on a sequence of n uniform random points in (0,1)d (d∈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∈(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
Keywords:Random spatial graphs, Network evolution, Variance asymptotics, Martingale differences.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1016/j.spa.2008.09.006
Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Stochastic processes and their applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic processes and their applications, 119(6), 2009, 10.1016/j.spa.2008.09.006
Date accepted:No date available
Date deposited:31 January 2013
Date of first online publication:June 2009
Date first made open access:No date available

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