{
  "id": "1210.4278",
  "version": "v1",
  "published": "2012-10-16T07:33:39.000Z",
  "updated": "2012-10-16T07:33:39.000Z",
  "title": "Stationary correlations for the 1D KPZ equation",
  "authors": [
    "Takashi Imamura",
    "Tomohiro Sasamoto"
  ],
  "comment": "38 pages, 5 figures",
  "journal": "J. Stat. Phys. 150, 908-939 (2013)",
  "doi": "10.1007/s10955-013-0710-3",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-16T07:33:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "1d kpz equation",
      "stationary correlations",
      "study exact stationary properties",
      "initial condition",
      "space-time two-point correlation function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2013,
      "month": "Mar",
      "volume": 150,
      "number": 5,
      "pages": 908
    },
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JSP...150..908I"
    }
  }
}