{
  "id": "2307.11029",
  "version": "v1",
  "published": "2023-07-20T17:02:54.000Z",
  "updated": "2023-07-20T17:02:54.000Z",
  "title": "Fluctuation Moments for Regular Functions of Wigner Matrices",
  "authors": [
    "Jana Reker"
  ],
  "comment": "52 pages (including appendix), 20 figures",
  "categories": [
    "math.PR",
    "math.CO",
    "math.OA"
  ],
  "abstract": "We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of [Male, Mingo, Pech\\'e, Speicher 2022], showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem obtained recently in the companion paper [Reker 2023].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-20T17:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52",
      "46L54"
    ],
    "keywords": [
      "wigner matrices",
      "fluctuation moments",
      "regular functions",
      "functional central limit theorem",
      "second-order free probability theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}