{
  "id": "0912.2499",
  "version": "v2",
  "published": "2009-12-13T13:07:31.000Z",
  "updated": "2010-02-18T17:21:31.000Z",
  "title": "Universal sum and product rules for random matrices",
  "authors": [
    "Tim Rogers"
  ],
  "journal": "J. Math. Phys. 51, 093304 (2010)",
  "doi": "10.1063/1.3481569",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact and universal expressions are found in the high-dimension limit for the quaternionic Green's functions of random matrices with independent entries when summed or multiplied with deterministic matrices. From these, the limiting spectral density can be accurately predicted.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-18T17:21:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "02.10.Yn",
      "02.30.Mv",
      "02.50.-r"
    ],
    "keywords": [
      "random matrices",
      "universal sum",
      "product rules",
      "quaternionic greens functions",
      "mean spectral density"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2010,
      "month": "Sep",
      "volume": 51,
      "number": 9,
      "pages": 3304
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JMP....51i3304R"
    }
  }
}