# Explicit laws of large numbers for random nearest-neighbour-type graphs

Wade, Andrew
(2007)
*Explicit laws of large numbers for random nearest-neighbour-type graphs.*
Advances in Applied Probability, 39 (2).
pp. 326-342.
ISSN 0001-8678

## Abstract

Under the unifying umbrella of a general result of Penrose & Yukich [Ann. Appl. Probab., (2003) 13, 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 in 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 |
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ID code: | 34458 |

Keywords: | nearest-neighbour-type graph, law of large numbers, spanning forest, spatial network evolution, explicit laws, large numbers, random, Probabilities. Mathematical statistics, Applied Mathematics, Statistics and Probability |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date deposited: | 04 Nov 2011 12:51 |

Last modified: | 22 Mar 2017 11:44 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/34458 |

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