{
  "id": "1911.00092",
  "version": "v1",
  "published": "2019-10-31T20:26:55.000Z",
  "updated": "2019-10-31T20:26:55.000Z",
  "title": "Logarithmic variance for the height function of square-ice",
  "authors": [
    "Hugo Duminil-Copin",
    "Matan Harel",
    "Benoit Laslier",
    "Aran Raoufi",
    "Gourab Ray"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this article, we prove that the height function associated with the square-ice model (i.e.~the six-vertex model with $a=b=c=1$ on the square lattice), or, equivalently, of the uniform random homomorphisms from $\\mathbb Z^2$ to $\\mathbb Z$, has logarithmic variance. This establishes a strong form of roughness of this height function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-31T20:26:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "height function",
      "logarithmic variance",
      "uniform random homomorphisms",
      "square-ice model",
      "six-vertex model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}