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

Andrew Wade

Research output: Contribution to journalArticle

22 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)326-342
Number of pages17
JournalAdvances in Applied Probability
Volume39
Issue number2
DOIs
Publication statusPublished - Jun 2007

Keywords

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

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