{
  "id": "1301.0938",
  "version": "v2",
  "published": "2013-01-05T20:05:02.000Z",
  "updated": "2013-01-09T11:12:00.000Z",
  "title": "Spectral norm of random Toeplitz matrices",
  "authors": [
    "Malika Kharouf"
  ],
  "comment": "This paper has been withdrawn by the author for improvement",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work, we consider symmetric random Toeplitz matrices $T_n$ generated by i.i.d. zero mean random variables ${X_k}$ satisfying the moment conditions: $E|X_k|^2=1$ and $\\E|X_1|^n \\le n^{\\sqrt{n}}$ for all $n\\ge 3$. We prove that the largest eigenvalue of $T_n$ scaled by $\\sqrt{n log(n)}$ converges almost surely to $1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-09T11:12:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "60F05"
    ],
    "keywords": [
      "spectral norm",
      "zero mean random variables",
      "symmetric random toeplitz matrices",
      "moment conditions",
      "largest eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.0938K"
    }
  }
}