Abstract
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 L
p
sense) for the total power-weighted length of several nearest-neighbour-type graphs on random point sets in ℝ
d
, 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
4 articles.
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