{
  "id": "1401.1081",
  "version": "v1",
  "published": "2014-01-06T13:54:49.000Z",
  "updated": "2014-01-06T13:54:49.000Z",
  "title": "Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz",
  "authors": [
    "Pierre Le Doussal"
  ],
  "comment": "27 pages, 3 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show how our previous result based on the replica Bethe ansatz for the Kardar Parisi Zhang (KPZ) equation with the \"half-flat\" initial condition leads to the Airy$_2$ to Airy$_1$ (i.e. GUE to GOE) universal crossover one-point height distribution in the limit of large time. Equivalently, we obtain the distribution of the free energy of a long directed polymer (DP) in a random potential with one fixed endpoint and the other one on a half-line. We then generalize to a DP when each endpoint is free on its own half-line. It amounts, in the limit of large time, to obtain the distribution of the maximum of the transition process Airy$_{2\\to 1}$ (minus a half-parabola) on a half line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-06T13:54:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "replica bethe ansatz",
      "flat initial conditions",
      "kpz equation",
      "universal crossover one-point height distribution",
      "large time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2014/04/P04018",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2014,
      "month": "Apr",
      "volume": 2014,
      "number": 4,
      "pages": "04018"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JSMTE..04..018L"
    }
  }
}