{
  "id": "1912.10261",
  "version": "v1",
  "published": "2019-12-21T12:57:27.000Z",
  "updated": "2019-12-21T12:57:27.000Z",
  "title": "Poisson statistics for Gibbs measures at high temperature",
  "authors": [
    "Gaultier Lambert"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a gas of N particles with a general two-body interaction and confined by an external potential in the mean field or high temperature regime, that is when the inverse temperature satisfies $\\beta N \\to \\kappa \\ge 0$ as $N\\to+\\infty$. We show that under general conditions on the interaction and the potential, the local fluctuations are described by a Poisson point process in the large N limit. We present applications to Coulomb and Riesz gases on $\\mathbb{R}^n$ for any $n\\ge 1$, as well as to the edge behavior of $\\beta$-ensembles on $\\mathbb{R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-21T12:57:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60G70",
      "60G55",
      "60F10"
    ],
    "keywords": [
      "gibbs measures",
      "poisson statistics",
      "general two-body interaction",
      "high temperature regime",
      "inverse temperature satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}