{
  "id": "math/9807134",
  "version": "v1",
  "published": "1998-07-24T07:48:13.000Z",
  "updated": "1998-07-24T07:48:13.000Z",
  "title": "Non-Gaussian Surface Pinned by a Weak Potential",
  "authors": [
    "J. -D. Deuschel",
    "Y. Velenik"
  ],
  "comment": "19 pages, 2 figures",
  "journal": "Probab. Theory Related Fields, Vol. 116, Nr. 3 (2000) , p. 359--377",
  "doi": "10.1007/s004400070004",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a model of a two-dimensional interface of the SOS type, with finite-range, even, strictly convex, twice continuously differentiable interactions. We prove that, under an arbitrarily weak potential favouring zero-height, the surface has finite mean square heights. We consider the cases of both square well and $\\delta$ potentials. These results extend previous results for the case of nearest-neighbours Gaussian interactions in \\cite{DMRR} and \\cite{BB}. We also obtain estimates on the tail of the height distribution implying, for example, existence of exponential moments. In the case of the $\\delta$ potential, we prove a spectral gap estimate for linear functionals. We finally prove exponential decay of the two-point function (1) for strong $\\delta$-pinning and the above interactions, and (2) for arbitrarily weak $\\delta$-pinning, but with finite-range Gaussian interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-07-24T07:48:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-gaussian surface",
      "finite mean square heights",
      "spectral gap estimate",
      "nearest-neighbours gaussian interactions",
      "arbitrarily weak potential favouring zero-height"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......7134D"
    }
  }
}