{
  "id": "2003.05906",
  "version": "v1",
  "published": "2020-03-12T17:12:55.000Z",
  "updated": "2020-03-12T17:12:55.000Z",
  "title": "Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$",
  "authors": [
    "Emilia Alvarez",
    "Nina C. Snaith"
  ],
  "comment": "28 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.NT"
  ],
  "abstract": "We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, $N$, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-12T17:12:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "11M06"
    ],
    "keywords": [
      "characteristic polynomials",
      "logarithmic derivative",
      "unitary random matrices",
      "symplectic random matrices",
      "asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}