{
  "id": "math-ph/0003043",
  "version": "v1",
  "published": "2000-03-29T16:52:25.000Z",
  "updated": "2000-03-29T16:52:25.000Z",
  "title": "On the Law of Addition of Random Matrices",
  "authors": [
    "L. Pastur",
    "V. Vasilchuk"
  ],
  "comment": "41 pages, submitted to Commun. Math. Phys",
  "doi": "10.1007/s002200000264",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e. $A_{n}+U_{n}^{\\ast}B_{n}U_{n}$) is studied in the limit of large matrix order $n$. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of $A_{n}$ and $B_{n}$ is obtained and studied. Keywords: random matrices, eigenvalue distribution",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-29T16:52:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C20",
      "60B12",
      "60G57"
    ],
    "keywords": [
      "random matrices",
      "large matrix order",
      "eigenvalue distribution",
      "limiting eigenvalue measures",
      "stieltjes transform"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2000,
      "volume": 214,
      "number": 2,
      "pages": 249
    },
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000CMaPh.214..249P"
    }
  }
}