{
  "id": "1311.2016",
  "version": "v1",
  "published": "2013-11-08T16:37:57.000Z",
  "updated": "2013-11-08T16:37:57.000Z",
  "title": "Local semicircle law with imprimitive variance matrix",
  "authors": [
    "Oskari Ajanki",
    "Laszlo Erdos",
    "Torben Krüger"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue $ -1 $. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices $ \\boldsymbol{\\mathrm{X}}^\\ast \\boldsymbol{\\mathrm{X}} $, where the variances of the entries of $ \\boldsymbol{\\mathrm{X}} $ may vary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-08T16:37:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60B20"
    ],
    "keywords": [
      "local semicircle law",
      "imprimitive variance matrix",
      "optimal local marchenko-pastur law",
      "sample covariance matrices",
      "short proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.2016A"
    }
  }
}