Professor Andrew Wade andrew.wade@durham.ac.uk
Professor
Explicit laws of large numbers for random nearest-neighbour-type graphs
Wade, Andrew R.
Authors
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.
Citation
Wade, A. R. (2007). Explicit laws of large numbers for random nearest-neighbour-type graphs. Advances in Applied Probability, 39(2), 326-342. https://doi.org/10.1239/aap/1183667613
Journal Article Type | Article |
---|---|
Publication Date | Jun 1, 2007 |
Deposit Date | Oct 4, 2012 |
Publicly Available Date | Mar 29, 2024 |
Journal | Advances in Applied Probability |
Print ISSN | 0001-8678 |
Electronic ISSN | 1475-6064 |
Publisher | Applied Probability Trust |
Peer Reviewed | Peer Reviewed |
Volume | 39 |
Issue | 2 |
Pages | 326-342 |
DOI | https://doi.org/10.1239/aap/1183667613 |
Keywords | Nearest-neighbour-type graph, Law of large numbers, Spanning forest, Spatial network evolution. |
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