{
  "id": "1804.08214",
  "version": "v1",
  "published": "2018-04-23T01:25:30.000Z",
  "updated": "2018-04-23T01:25:30.000Z",
  "title": "Poisson statistics at the edge of Gaussian $β$-ensemble at high temperature",
  "authors": [
    "Cambyse Pakzad"
  ],
  "comment": "35 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the asymptotic edge statistics of the Gaussian $\\beta$-ensemble, a collection of $n$ particles, as the inverse temperature $\\beta$ tends to zero as $n$ tends to infinity. In a certain decay regime of $\\beta$, the associated extreme point process is proved to converge in distribution to a Poisson point process as $n\\to +\\infty$. We also extend a well known result on Poisson limit for Gaussian extremes by showing the existence of an edge regime that we did not find in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T01:25:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60F05",
      "60G70"
    ],
    "keywords": [
      "poisson statistics",
      "high temperature",
      "asymptotic edge statistics",
      "poisson point process",
      "associated extreme point process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}