{
  "id": "1512.04910",
  "version": "v1",
  "published": "2015-12-15T19:42:06.000Z",
  "updated": "2015-12-15T19:42:06.000Z",
  "title": "Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation",
  "authors": [
    "Baruch Meerson",
    "Eytan Katzav",
    "Arkady Vilenkin"
  ],
  "comment": "11 one-column pages, including Supplemental Material, 3 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We evaluate the probability distribution $\\mathcal{P}(H)$ of large deviations $H$ of the evolving surface height $h(x,t)$ in the Kardar-Parisi-Zhang (KPZ) equation in one dimension when starting from a flat interface. We also determine the optimal history of the interface, conditioned on reaching the height $H$ at time $t$. The tails of $\\mathcal{P}(H)$ behave, at arbitrary time $t>0$, and in a proper moving frame, as $-\\ln \\mathcal{P}(H)\\sim |H|^{5/2}$ and $\\sim |H|^{3/2}$. The $3/2$ tail coincides with the asymptotic of the Gaussian orthogonal ensemble Tracy-Widom distribution, previously only observed at long times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T19:42:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviations",
      "kardar-parisi-zhang equation",
      "gaussian orthogonal ensemble tracy-widom distribution",
      "flat interface",
      "optimal history"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}