{
  "id": "1606.03076",
  "version": "v1",
  "published": "2016-06-09T19:32:02.000Z",
  "updated": "2016-06-09T19:32:02.000Z",
  "title": "Convergence Rate for Spectral Distribution of Addition of Random Matrices",
  "authors": [
    "Zhigang Bao",
    "Laszlo Erdos",
    "Kevin Schnelli"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $A$ and $B$ be two $N$ by $N$ deterministic Hermitian matrices and let $U$ be an $N$ by $N$ Haar distributed unitary matrix. It is well known that the spectral distribution of the sum $H=A+UBU^*$ converges weakly to the free additive convolution of the spectral distributions of $A$ and $B$, as $N$ tends to infinity. We establish the optimal convergence rate ${\\frac{1}{N}}$ in the bulk of the spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-09T19:32:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral distribution",
      "random matrices",
      "optimal convergence rate",
      "deterministic hermitian matrices",
      "haar distributed unitary matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}