{
  "id": "1909.03841",
  "version": "v1",
  "published": "2019-09-09T13:19:54.000Z",
  "updated": "2019-09-09T13:19:54.000Z",
  "title": "Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media",
  "authors": [
    "Alexander K. Hartmann",
    "Alexandre Krajenbrink",
    "Pierre Le Doussal"
  ],
  "comment": "13 pages, 8 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "physics.comp-ph"
  ],
  "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. The short time behavior is investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations, showing a spectacular agreement with the analytical expressions. The flat and stationary initial conditions are studied in the full space, together with the droplet initial condition in the half-space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-09T13:19:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "directed polymer",
      "large deviations",
      "kardar-parisi-zhang equation",
      "random media",
      "short time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}