{
  "id": "0907.4279",
  "version": "v2",
  "published": "2009-07-24T13:12:36.000Z",
  "updated": "2009-09-09T13:40:06.000Z",
  "title": "Scaling limits for critical inhomogeneous random graphs with finite third moments",
  "authors": [
    "Shankar Bhamidi",
    "Remco van der Hofstad",
    "Johan van Leeuwaarden"
  ],
  "comment": "Final version",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent $\\tau$ satisfies $\\tau>4$. We see that the sizes of the (rescaled) components converge to the excursion lengths of an inhomogeneous Brownian motion, extending results of \\cite{Aldo97}. We rely heavily on martingale convergence techniques, and concentration properties of (super)martingales. This paper is part of a programme to study the critical behavior in inhomogeneous random graphs of so-called rank-1 initiated in \\cite{Hofs09a}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-09T13:40:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05C80"
    ],
    "keywords": [
      "critical inhomogeneous random graphs",
      "finite third moments",
      "scaling limits",
      "martingale convergence techniques",
      "concentration properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4279B"
    }
  }
}