{
  "id": "1011.4014",
  "version": "v2",
  "published": "2010-11-17T18:16:47.000Z",
  "updated": "2011-01-28T11:13:27.000Z",
  "title": "Two-point generating function of the free energy for a directed polymer in a random medium",
  "authors": [
    "Sylvain Prolhac",
    "Herbert Spohn"
  ],
  "comment": "25 pages",
  "journal": "J. Stat. Mech. (2011) P01031",
  "doi": "10.1088/1742-5468/2011/01/P01031",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a 1+1 dimensional directed continuum polymer in a Gaussian delta-correlated space-time random potential. For this model the moments (= replica) of the partition function, Z(x,t), can be expressed in terms of the attractive delta-Bose gas on the line. Based on a recent study of the structure of the eigenfunctions, we compute the generating function for Z(x_1,t), Z(x_2,t) under a particular decoupling assumption and thereby extend recent results on the one-point generating function of the free energy to two points. It is established that in the long time limit the fluctuations of the free energy are governed by the two-point distribution of the Airy process, which further supports that the long time behavior of the KPZ equation is the same as derived previously for lattice growth models.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-28T11:13:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free energy",
      "two-point generating function",
      "random medium",
      "directed polymer",
      "gaussian delta-correlated space-time random potential"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2011,
      "month": "Jan",
      "volume": 2011,
      "number": 1,
      "pages": 1031
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JSMTE..01..031P"
    }
  }
}