{
  "id": "1506.03494",
  "version": "v1",
  "published": "2015-06-10T21:49:41.000Z",
  "updated": "2015-06-10T21:49:41.000Z",
  "title": "Poisson statistics for matrix ensembles at large temperature",
  "authors": [
    "Florent Benaych-Georges",
    "Sandrine Péché"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we consider $\\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\\frac{1}{Z_N(\\beta)}|\\Delta(\\lambda)|^\\beta e^{- \\frac{N\\beta}{4}\\sum_{i=1}^N\\lambda_i^2}d \\lambda,$$ in the regime where $\\beta\\to 0$ as $N\\to\\infty$. We briefly describe the global regime and then consider the local regime. In the case where $N\\beta$ stays bounded, we prove that the local eigenvalue statistics, in the vicinity of any real number, are asymptotically to those of a Poisson point process. In the case where $N\\beta\\to\\infty$, we prove a partial result in this direction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-10T21:49:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "60F05"
    ],
    "keywords": [
      "poisson statistics",
      "matrix ensembles",
      "large temperature",
      "local eigenvalue statistics",
      "poisson point process"
    ],
    "publication": {
      "doi": "10.1007/s10955-015-1340-8",
      "journal": "Journal of Statistical Physics",
      "year": 2015,
      "month": "Nov",
      "volume": 161,
      "number": 3,
      "pages": 633
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JSP...161..633B"
    }
  }
}