{
  "id": "1110.0108",
  "version": "v2",
  "published": "2011-10-01T15:20:35.000Z",
  "updated": "2012-10-19T08:12:49.000Z",
  "title": "Fast approach to the Tracy-Widom law at the edge of GOE and GUE",
  "authors": [
    "Iain M. Johnstone",
    "Zongming Ma"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/11-AAP819 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2012, Vol. 22, No. 5, 1962-1988",
  "doi": "10.1214/11-AAP819",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an $O(N^{-2/3})$ rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Numerical work shows that the suggested constants yield reasonable approximations, even for surprisingly small values of N.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-19T08:12:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tracy-widom law",
      "fast approach",
      "largest eigenvalue distributions",
      "constants yield reasonable approximations",
      "gaussian unitary"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0108J"
    }
  }
}