Wade, Andrew R. (2007) 'Explicit laws of large numbers for random nearest-neighbour-type graphs.', Advances in applied probability., 39 (2). pp. 326-342.
Under the unifying umbrella of a general result of Penrose and Yukich (Annals of Applied Probability 13 (2003), 277-303) we give laws of large numbers (in the Lp sense) for the total power-weighted length of several nearest-neighbour-type graphs on random point sets in ℝd, d ∈ ℕ. Some of these results are known; some are new. We give limiting constants explicitly, where previously they have been evaluated in less generality or not at all. The graphs we consider include the k-nearest-neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the on-line nearest-neighbour graph.
|Keywords:||Nearest-neighbour-type graph, Law of large numbers, Spanning forest, Spatial network evolution.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1239/aap/1183667613|
|Date accepted:||No date available|
|Date deposited:||13 February 2013|
|Date of first online publication:||June 2007|
|Date first made open access:||No date available|
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