{
  "id": "2010.08922",
  "version": "v1",
  "published": "2020-10-18T05:50:30.000Z",
  "updated": "2020-10-18T05:50:30.000Z",
  "title": "On the permanent of a random symmetric matrix",
  "authors": [
    "Matthew Kwan",
    "Lisa Sauermann"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let $M_{n}$ denote a random symmetric $n\\times n$ matrix, whose entries on and above the diagonal are i.i.d. Rademacher random variables (taking values $\\pm 1$ with probability $1/2$ each). Resolving a conjecture of Vu, we prove that the permanent of $M_{n}$ has magnitude $n^{n/2+o(n)}$ with probability $1-o(1)$. Our result can also be extended to more general models of random matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-18T05:50:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random symmetric matrix",
      "rademacher random variables",
      "probability",
      "random matrices",
      "general models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}