{
  "id": "math/0111036",
  "version": "v2",
  "published": "2001-11-02T23:46:57.000Z",
  "updated": "2002-03-28T01:03:44.000Z",
  "title": "Fluctuations in the composite regime of a disordered growth model",
  "authors": [
    "Janko Gravner",
    "Craig A. Tracy",
    "Harold Widom"
  ],
  "comment": "33 pages, 2 figures",
  "journal": "Commun. Math. Phys. 229 (2002), 433-458.",
  "doi": "10.1007/s00220-002-0682-7",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$ adopts the height above the site to its left if the latter height is larger, (2) otherwise, the height above $x$ increases by 1 with probability $p_x$. We assume that $p_x$ are chosen independently at random with a common distribution $F$, and that the initial state is such that the origin is far above the other sites. Provided that the tails of the distribution $F$ at its right edge are sufficiently thin, there exists a nontrivial composite regime in which the fluctuations of this interface are governed by extremal statistics of $p_x$. In the quenched case, the said fluctuations are asymptotically normal, while in the annealed case they satisfy the appropriate extremal limit law.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-03-28T01:03:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "05A16",
      "33E17",
      "60K37",
      "60G70",
      "82C44"
    ],
    "keywords": [
      "disordered growth model",
      "fluctuations",
      "appropriate extremal limit law",
      "one-dimensional integer lattice",
      "nontrivial composite regime"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2002,
      "volume": 229,
      "number": 3,
      "pages": 433
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002CMaPh.229..433G"
    }
  }
}