{
  "id": "1610.07391",
  "version": "v1",
  "published": "2016-10-24T12:50:28.000Z",
  "updated": "2016-10-24T12:50:28.000Z",
  "title": "Percolation results for the Continuum Random Cluster Model",
  "authors": [
    "Pierre Houdebert"
  ],
  "comment": "16 pages, 0 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the number of connected components in the random structure. We prove for a large class of parameters that percolation occurs for $z$ large enough and does not occur for $z$ small enough. An application to the phase transition of the Widom-Rowlinson model with random radii is given. Our main tools are stochastic domination properties, a fine study of the interaction of the model and a Fortuin-Kasteleyn representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-24T12:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60G10",
      "60G55",
      "60G57",
      "60G60",
      "60K35",
      "82B21",
      "82B26",
      "82B43"
    ],
    "keywords": [
      "continuum random cluster model",
      "percolation results",
      "standard boolean model",
      "stochastic domination properties",
      "gibbs modification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}