{
  "id": "1811.04055",
  "version": "v1",
  "published": "2018-11-09T18:29:25.000Z",
  "updated": "2018-11-09T18:29:25.000Z",
  "title": "Cusp Universality for Random Matrices II: The Real Symmetric Case",
  "authors": [
    "Giorgio Cipolloni",
    "László Erdős",
    "Torben Krüger",
    "Dominik Schröder"
  ],
  "comment": "49 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the complex Hermitian symmetry class, this completes the last remaining case of the Wigner-Dyson-Mehta universality conjecture after bulk and edge universalities have been established in the last years. We extend the recent Dyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp regime using the optimal local law from [arXiv:1809.03971] and the accurate local shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752]. We also present a novel method to improve the estimate on eigenvalue rigidity via the maximum principle of the heat flow related to the Dyson Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T18:29:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "real symmetric case",
      "cusp universality",
      "random matrices",
      "accurate local shape analysis",
      "complex hermitian symmetry class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}