{
  "id": "1210.2681",
  "version": "v3",
  "published": "2012-10-09T17:59:51.000Z",
  "updated": "2013-09-20T13:35:21.000Z",
  "title": "Spectral measures of powers of random matrices",
  "authors": [
    "Elizabeth Meckes",
    "Mark Meckes"
  ],
  "comment": "v3: Minor changes in response to referee comments. To appear in Electron. Commun. Probab",
  "journal": "Electron. Commun. Probab. 18 (2013) no. 78, 1-13",
  "doi": "10.1214/ECP.v18-2551",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "This paper considers the empirical spectral measure of a power of a random matrix drawn uniformly from one of the compact classical matrix groups. We give sharp bounds on the $L_p$-Wasserstein distances between this empirical measure and the uniform measure on the circle, which show a smooth transition in behavior when the power increases and yield rates on almost sure convergence when the dimension grows. Along the way, we prove the sharp logarithmic Sobolev inequality on the unitary group.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-09-20T13:35:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral measure",
      "random matrices",
      "sharp logarithmic sobolev inequality",
      "compact classical matrix groups",
      "random matrix drawn"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.2681M"
    }
  }
}