### Abstract

Language | English |
---|---|

Pages | 326-342 |

Number of pages | 17 |

Journal | Advances in Applied Probability |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2007 |

### Fingerprint

### Keywords

- nearest-neighbour-type graph
- law of large numbers
- spanning forest
- spatial network evolution
- explicit laws
- large numbers
- random

### Cite this

*Advances in Applied Probability*,

*39*(2), 326-342. https://doi.org/10.1239/aap/1183667613

}

*Advances in Applied Probability*, vol. 39, no. 2, pp. 326-342. https://doi.org/10.1239/aap/1183667613

**Explicit laws of large numbers for random nearest-neighbour-type graphs.** / Wade, Andrew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Explicit laws of large numbers for random nearest-neighbour-type graphs

AU - Wade, Andrew

PY - 2007/6

Y1 - 2007/6

N2 - 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.

AB - 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.

KW - nearest-neighbour-type graph

KW - law of large numbers

KW - spanning forest

KW - spatial network evolution

KW - explicit laws

KW - large numbers

KW - random

UR - http://projecteuclid.org/euclid.aap/1183667613

UR - http://arxiv.org/abs/math/0603559

U2 - 10.1239/aap/1183667613

DO - 10.1239/aap/1183667613

M3 - Article

VL - 39

SP - 326

EP - 342

JO - Advances in Applied Probability

T2 - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 2

ER -