{
  "id": "1802.02106",
  "version": "v1",
  "published": "2018-02-06T17:59:57.000Z",
  "updated": "2018-02-06T17:59:57.000Z",
  "title": "High-precision simulation of the height distribution for the KPZ equation",
  "authors": [
    "Alexander K. Hartmann",
    "Pierre Le Doussal",
    "Satya N. Majumdar",
    "Alberto Rosso",
    "Gregory Schehr"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T17:59:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "height distribution",
      "kpz equation",
      "high-precision simulation",
      "full scaling form remains",
      "importance sampling approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}