{
  "id": "1005.4471",
  "version": "v2",
  "published": "2010-05-25T02:54:24.000Z",
  "updated": "2011-11-29T15:57:46.000Z",
  "title": "Upper tails for triangles",
  "authors": [
    "Bobby DeMarco",
    "Jeff Kahn"
  ],
  "comment": "10 pages",
  "doi": "10.1002/rsa.20382",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "With $\\xi$ the number of triangles in the usual (Erd\\H{o}s-R\\'enyi) random graph $G(m,p)$, $p>1/m$ and $\\eta>0$, we show (for some $C_{\\eta}>0$) $$\\Pr(\\xi> (1+\\eta)\\E \\xi) < \\exp[-C_{\\eta}\\min{m^2p^2\\log(1/p),m^3p^3}].$$ This is tight up to the value of $C_{\\eta}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-29T15:57:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "05C80"
    ],
    "keywords": [
      "upper tails",
      "random graph"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4471D"
    }
  }
}