{
  "id": "math/0308190",
  "version": "v1",
  "published": "2003-08-20T10:31:16.000Z",
  "updated": "2003-08-20T10:31:16.000Z",
  "title": "Central limit theorems in Random cluster and Potts Models",
  "authors": [
    "Olivier Garet"
  ],
  "comment": "version du 19 aout 2003",
  "journal": "Mathematical Physics Electronic Journal 11 (2005) paper 4 (27 pages)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2. Particularly, we can take r(q)=p_g^* for d=2, which is commonly conjectured to be equal to p_c. These results are used to prove a q-dimensional central limit theorems relative to the fluctuation of the empirical measures for the ground Gibbs measures of the q-state Potts model at very low temperature and the Gibbs measures which reside in the convex hull of them. A similar central limit theorem is also given in the high temperature regime. Some particular properties of the Ising model are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-08-20T10:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B20",
      "82B43"
    ],
    "keywords": [
      "potts model",
      "gibbs measures",
      "similar central limit theorem",
      "normal central limit behaviour",
      "q-dimensional central limit theorems relative"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8190G"
    }
  }
}