{
  "id": "2104.11494",
  "version": "v1",
  "published": "2021-04-23T09:31:23.000Z",
  "updated": "2021-04-23T09:31:23.000Z",
  "title": "The hard-to-soft edge transition: exponential moments, central limit theorems and rigidity",
  "authors": [
    "Christophe Charlier",
    "Jonatan Lenells"
  ],
  "comment": "46 pages, 7 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\\alpha$. For this point process, we obtain 1) exponential moment asymptotics, up to and including the constant term, 2) asymptotics for the expectation and variance of the counting function, 3) several central limit theorems and 4) a global rigidity upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-23T09:31:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorems",
      "hard-to-soft edge transition",
      "global rigidity upper bound",
      "exponential moment asymptotics",
      "large random matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}