{
  "id": "1407.2759",
  "version": "v3",
  "published": "2014-07-10T11:28:48.000Z",
  "updated": "2016-02-18T22:48:23.000Z",
  "title": "Universality in several-matrix models via approximate transport maps",
  "authors": [
    "Alessio Figalli",
    "Alice Guionnet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices, i.e., they are given by the Sine-kernel in the bulk and the Tracy-Widom distribution at the edge. Moreover, we prove universality for the local statistics of eigenvalues of self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-28T13:38:16.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-02-18T22:48:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universality",
      "construct approximate transport maps",
      "goe matrices",
      "local statistics",
      "independent gue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2759F"
    }
  }
}