{
  "id": "1312.0037",
  "version": "v2",
  "published": "2013-11-29T23:00:37.000Z",
  "updated": "2014-11-07T22:10:08.000Z",
  "title": "On the limiting spectral distribution for a large class of random matrices with correlated entries",
  "authors": [
    "Florence Merlevede",
    "Magda Peligrad",
    "Marwa Banna"
  ],
  "comment": "27 pages. In this version we shorten the title and removed one of the conditions used in the previous version",
  "categories": [
    "math.PR"
  ],
  "abstract": "For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure. This class contains both cases of short and long range dependent random fields. The technique is based on a blend of blocking procedure and Lindeberg's method. This method leads to a variety of interesting asymptotic results for matrices with dependent entries, including applications to linear processes as well as nonlinear Volterra-type processes entries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-29T23:00:37.000Z",
      "title": "On the universality of the limiting spectral distribution for a large class of random matrices with correlated entries",
      "abstract": "We develop a method for studying the eigenvalue distribution for a n by n symmetric matrix with dependent entries. The technique is based on a blend of blocking procedure and Lindeberg's method. For a large class of random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical spectral distributions can be obtained by analyzing a Gaussian matrix with the same covariance structure. This method leads to a variety of interesting asymptotic results for matrices with dependent entries, including applications to linear processes as well as nonlinear Volterra-type processes entries.",
      "comment": "27 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-07T22:10:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60G60",
      "60G10",
      "62E20"
    ],
    "keywords": [
      "limiting spectral distribution",
      "random matrices",
      "large class",
      "correlated entries",
      "universality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0037M"
    }
  }
}