{
  "id": "1503.06738",
  "version": "v1",
  "published": "2015-03-23T17:29:42.000Z",
  "updated": "2015-03-23T17:29:42.000Z",
  "title": "Joint Convergence of Random Quadrangulations and Their Cores",
  "authors": [
    "Louigi Addario-Berry",
    "Yuting Wen"
  ],
  "comment": "30 pages, 5 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We show that a uniform quadrangulation, its largest 2-connected block, and its largest simple block jointly converge to the same Brownian map in distribution for the Gromov-Hausdorff-Prokhorov topology. We start by deriving a local limit theorem for the asymptotics of maximal block sizes, extending the result in \\cite{BFSS}. The resulting diameter bounds for pendant submaps of random quadrangulations straightforwardly lead to Gromov-Hausdorff convergence. To extend the convergence to the Gromov-Hausdorff-Prokhorov topology, we show that exchangeable \"uniformly asymptotically negligible\" attachments of mass simply yield, in the limit, a deterministic scaling of the mass measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-23T17:29:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05C10"
    ],
    "keywords": [
      "random quadrangulations",
      "joint convergence",
      "largest simple block jointly converge",
      "gromov-hausdorff-prokhorov topology",
      "local limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150306738A"
    }
  }
}