{
  "id": "2008.01223",
  "version": "v1",
  "published": "2020-08-03T22:09:50.000Z",
  "updated": "2020-08-03T22:09:50.000Z",
  "title": "The characteristic polynomial of a random matrix",
  "authors": [
    "Sean Eberhard"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "Form an $n \\times n$ matrix by drawing entries independently from $\\{\\pm1\\}$ (or another fixed nontrivial finitely supported distribution in $\\mathbf{Z}$) and let $\\phi$ be the characteristic polynomial. Conditionally on the extended Riemann hypothesis, with high probability $\\phi$ is irreducible and $\\mathrm{Gal}(\\phi) \\geq A_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-03T22:09:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "11M50"
    ],
    "keywords": [
      "characteristic polynomial",
      "random matrix",
      "fixed nontrivial finitely supported distribution",
      "extended riemann hypothesis",
      "high probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}