{
  "id": "1305.5009",
  "version": "v3",
  "published": "2013-05-22T03:20:04.000Z",
  "updated": "2015-08-04T02:14:50.000Z",
  "title": "A transition of limiting distributions of large matchings in random graphs",
  "authors": [
    "Pu Gao",
    "Cristiane M. Sato"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We study the asymptotic distribution of the number of matchings of size $\\ell=\\ell(n)$ in $G(n,p)$ for a wide range of $p=p(n)\\in (0,1)$ and for every $1\\le \\ell\\le \\lfloor n/2\\rfloor$. We prove that this distribution changes from normal to log-normal as $\\ell$ increases, and we determine the critical value of $\\ell$, as a function of $n$ and $p$, at which the transition of the limiting distribution occurs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-28T01:48:32.000Z",
      "abstract": "We study the asymptotic distribution of the number of matchings of size $\\ell=\\ell(n)$ in $G(n,p)$ for a wide range of $p=p(n)\\in (0,1)$ and for every $1\\le \\ell\\le \\floor{n/2}$. We prove that this distribution changes from normal to log-normal as $\\ell$ increases, and we determine the critical value of $\\ell$, as a function of $n$ and $p$, at which the transition of the limiting distribution occurs.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-08-04T02:14:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large matchings",
      "random graphs",
      "transition",
      "asymptotic distribution",
      "wide range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5009G"
    }
  }
}