{
  "id": "1803.02151",
  "version": "v1",
  "published": "2018-03-06T12:57:50.000Z",
  "updated": "2018-03-06T12:57:50.000Z",
  "title": "A functional CLT for partial traces of random matrices",
  "authors": [
    "Jan Nagel"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we show a functional central limit theorem for the sum of the first $\\lfloor t n \\rfloor$ diagonal elements of $f(Z)$ as a function in $t$, for $Z$ a random real symmetric or complex Hermitian $n\\times n$ matrix. The result holds for orthogonal or unitarily invariant distributions of $Z$, in the cases when the linear eigenvalue statistic $\\operatorname{tr} f(Z)$ satisfies a CLT. The limit process interpolates between the fluctuations of individual matrix elements as $f(Z)_{1,1}$ and of the linear eigenvalue statistic. It can also be seen as a functional CLT for processes of randomly weighted measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-06T12:57:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional clt",
      "random matrices",
      "partial traces",
      "linear eigenvalue statistic",
      "functional central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}