Wade, Andrew R. (2007) 'Explicit laws of large numbers for random nearest-neighbour-type graphs.', Advances in applied probability., 39 (2). pp. 326-342.
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 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.
| Item Type: | Article |
|---|---|
| Keywords: | Nearest-neighbour-type graph, Law of large numbers, Spanning forest, Spatial network evolution. |
| Full text: | (AM) Accepted Manuscript Download PDF (568Kb) |
| Status: | Peer-reviewed |
| 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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