{
  "id": "1502.04238",
  "version": "v1",
  "published": "2015-02-14T20:06:41.000Z",
  "updated": "2015-02-14T20:06:41.000Z",
  "title": "Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction",
  "authors": [
    "B. Jahnel",
    "C. Kuelske"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the Gibbs properties of the fuzzy Potts model on the d-dimensional torus with Kac interaction. We use a variational approach for profiles inspired by that of Fernandez, den Hollander and Mart{\\i}nez for their study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the torus. As our main result, we show that the mean-field thresholds dividing Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model. On the way to this result we prove a large deviation principle for color profiles with diluted total mass densities and use monotocity arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-14T20:06:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fuzzy potts model",
      "gibbs-non-gibbs transition",
      "sharp thresholds",
      "kac-type interaction",
      "diluted total mass densities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150204238J"
    }
  }
}