{
  "id": "1907.12308",
  "version": "v1",
  "published": "2019-07-29T09:54:21.000Z",
  "updated": "2019-07-29T09:54:21.000Z",
  "title": "Log-Sobolev inequality for the continuum Sine-Gordon model",
  "authors": [
    "Roland Bauerschmidt",
    "Thierry Bodineau"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We prove a multiscale generalisation of the Bakry--\\'Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an associated PDE well known in renormalisation theory: the Polchinski equation. It implies the usual Bakry--\\'Emery criterion, but we show that it remains effective for measures which are far from log-concave. Indeed, using our criterion, we prove that the massive continuum Sine-Gordon model with $\\beta < 6\\pi$ satisfies asymptotically optimal Log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-29T09:54:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "log-sobolev inequality",
      "satisfies asymptotically optimal log-sobolev inequalities",
      "usual bakry-emery criterion",
      "massive continuum sine-gordon model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}