{
  "id": "0712.3687",
  "version": "v1",
  "published": "2007-12-21T12:54:19.000Z",
  "updated": "2007-12-21T12:54:19.000Z",
  "title": "On the sphericity of scaling limits of random planar quadrangulations",
  "authors": [
    "Grégory Marc Miermont"
  ],
  "comment": "11pp, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a new proof of a theorem by Le Gall & Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of the notion of Gromov-Hausdorff convergence, called 1-regular convergence, that preserves topological properties of metric surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-21T12:54:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60F05",
      "60D05"
    ],
    "keywords": [
      "random planar quadrangulations",
      "scaling limits",
      "sphericity",
      "main geometric tool",
      "preserves topological properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3687M"
    }
  }
}