{
  "id": "2209.06010",
  "version": "v1",
  "published": "2022-09-13T14:01:21.000Z",
  "updated": "2022-09-13T14:01:21.000Z",
  "title": "Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices",
  "authors": [
    "Tom Claeys",
    "Johannes Forkel",
    "Jonathan P. Keating"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity. Our results are analogous to those that Fahs obtained for random unitary matrices in [14]. A key feature of the formulae we derive is that the phase transitions in the moments of moments are seen to depend on the symmetry group in question in a significant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-13T14:01:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "characteristic polynomials",
      "symplectic matrices",
      "random orthogonal",
      "random unitary matrices",
      "asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}