{
  "id": "1208.5100",
  "version": "v4",
  "published": "2012-08-25T05:07:29.000Z",
  "updated": "2013-07-04T14:58:55.000Z",
  "title": "Limiting Spectral Distribution of Sum of Unitary and Orthogonal Matrices",
  "authors": [
    "Anirban Basak",
    "Amir Dembo"
  ],
  "comment": "17 pages; changes in the presentation style, several minor changes in proofs",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the empirical eigenvalue measure for sum of $d$ independent Haar distributed $n$-dimensional unitary matrices, converge for $n \\to \\infty$ to the Brown measure of the free sum of $d$ Haar unitary operators. The same applies for independent Haar distributed $n$-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes transform of $T_n$ that is made in [Guionnet, Krishnapur, Zeitouni; Theorem 1].",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-07-04T14:58:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L53",
      "60B10",
      "60B20"
    ],
    "keywords": [
      "limiting spectral distribution",
      "independent haar",
      "dimensional unitary matrices",
      "haar unitary operators",
      "dimensional orthogonal matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.5100B"
    }
  }
}