Asymptotic theory for the multidimensional random online nearestneighbour graph
Wade, Andrew R. (2009) Asymptotic theory for the multidimensional random online nearestneighbour graph. Stochastic Processes and their Applications, 119 (6). pp. 18891911. ISSN 03044149 (https://doi.org/10.1016/j.spa.2008.09.006)
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Abstract
The online nearestneighbour 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 powerweighted edgelength 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→∞ largesample convergence result for the total powerweighted edgelength 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 Dates: DateEventJune 2009PublishedKeywords: random spatial graphs, network evolution, variance asymptotics, martingale dierences, statistics, Probabilities. Mathematical statistics, Mathematics, Modelling and Simulation, Applied Mathematics, Statistics and Probability Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > MathematicsDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Mrs Carolynne Westwood Date deposited: 12 Nov 2009 14:06 Last modified: 29 Jan 2023 03:10 URI: https://strathprints.strath.ac.uk/id/eprint/13393