{
  "id": "math/0607567",
  "version": "v2",
  "published": "2006-07-22T11:12:16.000Z",
  "updated": "2006-10-31T10:36:29.000Z",
  "title": "The topological structure of scaling limits of large planar maps",
  "authors": [
    "Jean-Francois Le Gall"
  ],
  "comment": "45 pages Second version with minor modifications",
  "doi": "10.1007/s00222-007-0059-9",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-31T10:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60D05",
      "05C12"
    ],
    "keywords": [
      "large planar maps",
      "scaling limits",
      "topological structure",
      "large bipartite planar maps",
      "limiting random compact metric space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2007,
      "month": "Jun",
      "volume": 169,
      "number": 3,
      "pages": 621
    },
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007InMat.169..621L"
    }
  }
}