{
  "id": "2212.10694",
  "version": "v1",
  "published": "2022-12-20T23:54:52.000Z",
  "updated": "2022-12-20T23:54:52.000Z",
  "title": "Fluctuations of eigenvector overlaps and the Berry conjecture for Wigner matrices",
  "authors": [
    "Lucas Benigni",
    "Giorgio Cipolloni"
  ],
  "comment": "16 pages, 6 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that any finite collection of quadratic forms (overlaps) of general deterministic matrices and eigenvectors of an $N\\times N$ Wigner matrix has joint Gaussian fluctuations. This can be viewed as the random matrix analogue of the Berry random wave conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-20T23:54:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "wigner matrix",
      "eigenvector overlaps",
      "berry conjecture",
      "berry random wave conjecture",
      "general deterministic matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}