{
  "id": "1902.10867",
  "version": "v1",
  "published": "2019-02-28T02:31:26.000Z",
  "updated": "2019-02-28T02:31:26.000Z",
  "title": "Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model",
  "authors": [
    "Amol Aggarwal"
  ],
  "comment": "59 pages, 3 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by the entropy solution to an explicit, non-linear conservation law that was predicted by Gwa-Spohn in 1992 and by Reshetikhin-Sridhar in 2018. Then, we show that the local statistics of this model around any continuity point of its limit shape are given by an infinite-volume, translation-invariant Gibbs measure of the appropriate slope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-28T02:31:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic six-vertex model",
      "limit shape",
      "local statistics",
      "arbitrary initial data",
      "non-linear conservation law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}