{
  "id": "1610.04195",
  "version": "v1",
  "published": "2016-10-13T18:36:58.000Z",
  "updated": "2016-10-13T18:36:58.000Z",
  "title": "Maximum of the Ginzburg-Landau fields",
  "authors": [
    "David Belius",
    "Wei Wu"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study two dimensional massless field in a box with potential $V\\left( \\nabla \\phi \\left( \\cdot \\right) \\right) $ and zero boundary condition, where $V$ is any symmetric and uniformly convex function. Naddaf-Spencer and Miller proved the macroscopic averages of this field converge to a continuum Gaussian free field. In this paper we prove the distribution of local marginal $\\phi \\left( x\\right) $, for any $x$ in the bulk, has a Gaussian tail. We further characterize the leading order of the maximum and dimension of high points of this field, thus generalize the results of Bolthausen-Deuschel-Giacomin and Daviaud for the discrete Gaussian free field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T18:36:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ginzburg-landau fields",
      "discrete gaussian free field",
      "continuum gaussian free field",
      "zero boundary condition",
      "uniformly convex function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}