{
  "id": "1406.3171",
  "version": "v2",
  "published": "2014-06-12T09:47:37.000Z",
  "updated": "2015-03-09T21:00:55.000Z",
  "title": "Joint large deviation result for empirical measures of the near intermediate coloured random geometric graphs",
  "authors": [
    "Kwabena Doku-Amponsah"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1312.6326",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove joint large deviation principle for the \\emph{ empirical pair measure} and \\emph{empirical locality measure} of the \\emph{near intermediate} coloured random geometric graph models, see (Canning \\& Penman, 2003), on $n$ points picked uniformly in $[0,1]^d,$ for $d\\in\\N.$ From this result we obtain large deviation principles for the \\emph{number of edges per vertex}, the \\emph{degree distribution and the proportion of isolated vertices } for the \\emph{near intermediate} random geometric graph models.% on $n$ vertices placed uniformly in $[0,1]^d,$ for $d\\in\\N.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-12T09:47:37.000Z",
      "title": "Large deviations for number of edges of near intermediate random geometric graphs",
      "abstract": "We find large deviation principle for the number of edges per vertex for the near intermediate random geometric graph models on n vertices placed uniformly in [0, 1]^d. In the course of the proof of this large deviation result we find joint large deviation principle for the empirical colour measure and the empirical pair measure of the coloured random geometric graphs. This graphs have been suggested by Canning and Penman(2003), as a possible extension to the randomly coloured random graphs.",
      "comment": "arXiv admin note: substantial text overlap with arXiv:1312.6326",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-09T21:00:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "05C80"
    ],
    "keywords": [
      "intermediate random geometric graph models",
      "joint large deviation principle",
      "coloured random geometric graphs",
      "large deviation result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3171D"
    }
  }
}