{
  "id": "1105.2556",
  "version": "v2",
  "published": "2011-05-12T19:51:51.000Z",
  "updated": "2012-02-07T18:53:12.000Z",
  "title": "Asymptotic eigenvalue distributions of block-transposed Wishart matrices",
  "authors": [
    "Teodor Banica",
    "Ion Nechita"
  ],
  "journal": "J. Theoret. Probab. 26 (2013), 855-869",
  "categories": [
    "math.PR",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "We study the partial transposition ${W}^\\Gamma=(\\mathrm{id}\\otimes \\mathrm{t})W\\in M_{dn}(\\mathbb C)$ of a Wishart matrix $W\\in M_{dn}(\\mathbb C)$ of parameters $(dn,dm)$. Our main result is that, with $d\\to\\infty$, the law of $m{W}^\\Gamma$ is a free difference of free Poisson laws of parameters $m(n\\pm 1)/2$. Motivated by questions in quantum information theory, we also derive necessary and sufficient conditions for these measures to be supported on the positive half line.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-07T18:53:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "46L54",
      "81P45"
    ],
    "keywords": [
      "asymptotic eigenvalue distributions",
      "block-transposed wishart matrices",
      "quantum information theory",
      "free poisson laws",
      "positive half line"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.2556B"
    }
  }
}