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

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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    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: 12 Dec 2013 00:36
      URI: http://strathprints.strath.ac.uk/id/eprint/13393

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