## 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 $R^d$, $d \in N$. 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.

Translated title of the contribution | Explicit laws of large numbers for random nearest-neighbour-type graphs |
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Original language | English |

Pages (from-to) | 326 - 342 |

Number of pages | 17 |

Journal | Advances in Applied Probability |

Volume | 39 (2) |

DOIs | |

Publication status | Published - Jun 2007 |