{
  "id": "2103.06730",
  "version": "v1",
  "published": "2021-03-11T15:23:48.000Z",
  "updated": "2021-03-11T15:23:48.000Z",
  "title": "Normal fluctuation in quantum ergodicity for Wigner matrices",
  "authors": [
    "Giorgio Cipolloni",
    "László Erdős",
    "Dominik Schröder"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the quadratic form of a general deterministic matrix on the eigenvectors of an $N\\times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large $N$ limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by [Marcinek, Yau 2020] and our recent multi-resolvent local laws [Cipolloni, Erd\\H{o}s, Schr\\\"oder 2020].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T15:23:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "wigner matrix",
      "quantum ergodicity",
      "normal fluctuation",
      "general deterministic matrix",
      "dyson brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}