{
  "id": "1712.00931",
  "version": "v1",
  "published": "2017-12-04T07:04:44.000Z",
  "updated": "2017-12-04T07:04:44.000Z",
  "title": "Central limit theorem for linear spectral statistics of deformed Wigner matrices",
  "authors": [
    "Hong Chang Ji",
    "Ji Oon Lee"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider large-dimensional Hermitian random matrices of the form $W=M+\\vartheta V$ where $M$ is a Wigner matrix and $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $M$. For a large class of diagonal matrices $V$, we prove that the fluctuations of linear spectral statistics of $W$ for analytic test function can be decomposed into that of $M$ and of $V$, and that each of those weakly converges to a Gaussian distribution. We also calculate the formulae for the means and variances of the limiting distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-04T07:04:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60F05",
      "15B52"
    ],
    "keywords": [
      "wigner matrix",
      "linear spectral statistics",
      "central limit theorem",
      "deformed wigner matrices",
      "diagonal matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}