{
  "id": "1701.03327",
  "version": "v1",
  "published": "2017-01-12T12:52:25.000Z",
  "updated": "2017-01-12T12:52:25.000Z",
  "title": "Entropic repulsion in $|\\nabla φ|^p$ surfaces: a large deviation bound for all $p\\geq 1$",
  "authors": [
    "Pietro Caputo",
    "Fabio Martinelli",
    "Fabio Lucio Toninelli"
  ],
  "comment": "14 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the $(2+1)$-dimensional generalized solid-on-solid (SOS) model, that is the random discrete surface with a gradient potential of the form $|\\nabla\\phi|^{p}$, where $p\\in [1,+\\infty]$. We show that at low temperature, for a square region $\\Lambda$ with side $L$, both under the infinite volume measure and under the measure with zero boundary conditions around $\\Lambda$, the probability that the surface is nonnegative in $\\Lambda$ behaves like $\\exp(-4\\beta\\tau_{p,\\beta} L H_p(L) )$, where $\\beta$ is the inverse temperature, $\\tau_{p,\\beta}$ is the surface tension at zero tilt, or step free energy, and $H_p(L)$ is the entropic repulsion height, that is the typical height of the field when a positivity constraint is imposed. This generalizes recent results obtained in \\cite{CMT} for the standard SOS model ($p=1$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-12T12:52:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation bound",
      "random discrete surface",
      "entropic repulsion height",
      "step free energy",
      "infinite volume measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}