{
  "id": "1508.07764",
  "version": "v1",
  "published": "2015-08-31T11:04:39.000Z",
  "updated": "2015-08-31T11:04:39.000Z",
  "title": "Energy solutions of KPZ are unique",
  "authors": [
    "M. Gubinelli",
    "N. Perkowski"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Energy solutions is a weak notion of solution to the KPZ equation which was introduced by Gon\\c{c}alves and Jara [ARMA 212 (2013)] to describe the large scale fluctuations of a wide class of weakly asymmetric particle systems. In this paper we prove that energy solutions of the periodic, stationary, stochastic Burgers equation are unique and in particular they coincide with the Hopf--Cole solution. To obtain uniqueness we use the reformulation of the energy solution concept given by Gubinelli and Jara [SPDE--AC 1 (2013)] and an observation by Funaki and Quastel [ArXiv:1407.7310].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-31T11:04:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic burgers equation",
      "energy solution concept",
      "weakly asymmetric particle systems",
      "large scale fluctuations",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807764G"
    }
  }
}