{
  "id": "math/0607545",
  "version": "v2",
  "published": "2006-07-21T15:53:36.000Z",
  "updated": "2010-11-11T09:08:39.000Z",
  "title": "Large deviation principles for empirical measures of colored random graphs",
  "authors": [
    "Kwabena Doku-Amponsah",
    "Peter Mörters"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP647 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2010, Vol. 20, No. 6, 1989-2021",
  "doi": "10.1214/09-AAP647",
  "categories": [
    "math.PR"
  ],
  "abstract": "For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erd\\H{o}s--R\\'{e}nyi graphs near criticality.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-11T09:08:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation principle",
      "empirical measures",
      "sparse colored random graphs",
      "neighborhood measure",
      "degree distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7545D"
    }
  }
}