{
  "id": "math/0603559",
  "version": "v2",
  "published": "2006-03-23T11:35:02.000Z",
  "updated": "2007-02-14T12:24:43.000Z",
  "title": "Explicit laws of large numbers for random nearest-neighbour type graphs",
  "authors": [
    "Andrew R. Wade"
  ],
  "comment": "18 pages, 2 figures; revised presentation",
  "journal": "Advances in Applied Probability, Vol. 39 (2007), no. 2, p. 326-342",
  "doi": "10.1239/aap/1183667613",
  "categories": [
    "math.PR"
  ],
  "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 $L^p$ 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-14T12:24:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60F25"
    ],
    "keywords": [
      "random nearest-neighbour type graphs",
      "large numbers",
      "explicit laws",
      "on-line nearest-neighbour graph",
      "k-nearest neighbours graph"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3559W"
    }
  }
}