{
  "id": "math/0510181",
  "version": "v1",
  "published": "2005-10-10T09:43:22.000Z",
  "updated": "2005-10-10T09:43:22.000Z",
  "title": "From Gumbel to Tracy-Widom",
  "authors": [
    "Kurt Johansson"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The Tracy-Widom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution $\\exp(-\\exp(-x))$, the Gumbel distribution and the Tracy-Widom distribution. There is a family of determinantal processes whose edge behaviour interpolates between a Poisson process with density $\\exp(-x)$ and the Airy kernel point process. This process can be obtained as a scaling limit of a grand canonical version of a random matrix model introduced by Moshe, Neuberger and Shapiro. We also consider the deformed GUE ensemble, $M=M_0+\\sqrt{2S} V$, with $M_0$ diagobal with independent elements and $V$ from GUE. Here we do not see a transition from Tracy-Widom to Gumbel, but rather a transition from Tracy-Widom to Gaussian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-10T09:43:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tracy-widom distribution",
      "airy kernel point process",
      "random matrix model",
      "edge behaviour interpolates",
      "classical extreme value distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10181J"
    }
  }
}