{
  "id": "1806.08751",
  "version": "v1",
  "published": "2018-06-22T16:25:57.000Z",
  "updated": "2018-06-22T16:25:57.000Z",
  "title": "Fluctuations for linear eigenvalue statistics of sample covariance random matrices",
  "authors": [
    "Giorgio Cipolloni",
    "László Erdős"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix $\\widetilde{W}$ and its minor $W$. We find that the fluctuation of this difference is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of $\\widetilde{W}$ and $W$. Unlike in a similar result for Wigner matrices [arXiv:1608.05163], for sample covariance matrices the fluctuation may entirely vanish and we identify these cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-22T16:25:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "sample covariance random matrices",
      "linear eigenvalue statistics",
      "fluctuation",
      "sample covariance matrix",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}