{
  "id": "math/0401115",
  "version": "v1",
  "published": "2004-01-12T13:35:20.000Z",
  "updated": "2004-01-12T13:35:20.000Z",
  "title": "Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees",
  "authors": [
    "David J. Aldous",
    "Gregory Miermont",
    "Jim Pitman"
  ],
  "comment": "16 pages",
  "journal": "Probability Theory and Related Fields 133 (2005) 1--17",
  "doi": "10.1007/s00440-004-0407-2",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotics of the $p$-mapping model of random mappings on $[n]$ as $n$ gets large, under a large class of asymptotic regimes for the underlying distribution $p$. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2003) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of ``attracting points'' to emerge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-12T13:35:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60F17"
    ],
    "keywords": [
      "inhomogeneous continuum random trees",
      "exploration process",
      "weak convergence",
      "random p-mappings",
      "random mappings"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1115A"
    }
  }
}