{
  "id": "1308.5516",
  "version": "v1",
  "published": "2013-08-26T08:54:34.000Z",
  "updated": "2013-08-26T08:54:34.000Z",
  "title": "Moderate deviations for spectral measures of random matrix ensembles",
  "authors": [
    "Jan Nagel"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the (weighted) spectral measure $\\mu_n$ of a $n\\times n$ random matrix, distributed according to a classical Gaussian, Laguerre or Jacobi ensemble, and show a moderate deviation principle for the standardised signed measure $\\sqrt{n/a_n}(\\mu_n -\\sigma)$. The centering measure $\\sigma$ is the weak limit of the empirical eigenvalue distribution and the rate function is given in terms of the $L^2$-norm of the density with respect to $\\sigma$. The proof involves the tridiagonal representations of the ensembles which provide us with a sequence of independent random variables and a link to orthogonal polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-26T08:54:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60F10"
    ],
    "keywords": [
      "random matrix ensembles",
      "spectral measure",
      "moderate deviation principle",
      "independent random variables",
      "rate function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.5516N"
    }
  }
}