{
  "id": "1306.1484",
  "version": "v2",
  "published": "2013-06-06T17:40:48.000Z",
  "updated": "2014-06-19T15:48:18.000Z",
  "title": "Modified logarithmic Sobolev inequalities for canonical ensembles",
  "authors": [
    "Max Fathi"
  ],
  "comment": "19 pages v2: a mistake has been corrected in the proof of Lemma 2.3 (formerly Lemma 2.8), and the presentation has been reworked",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we prove modified logarithmic Sobolev inequalities for canonical ensembles with superquadratic single-site potential. These inequalities were introduced by Bobkov and Ledoux, and are closely related to concentration of measure and transport-entropy inequalities. Our method is an adaptation of the iterated two-scale approach that was developed by Menz and Otto to prove the usual logarithmic Sobolev inequality in this context. As a consequence, we obtain convergence in Wasserstein distance $W_p$ for Kawasaki dynamics on the Ginzburg-Landau model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-19T15:48:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modified logarithmic sobolev inequalities",
      "canonical ensembles",
      "usual logarithmic sobolev inequality",
      "superquadratic single-site potential",
      "ginzburg-landau model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1484F"
    }
  }
}