{
  "id": "1407.8015",
  "version": "v2",
  "published": "2014-07-30T12:13:06.000Z",
  "updated": "2014-11-01T02:01:56.000Z",
  "title": "Edge Universality for Deformed Wigner Matrices",
  "authors": [
    "Ji Oon Lee",
    "Kevin Schnelli",
    "Horng-Tzer Yau"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider $N\\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for the matrix entries of $W$ and we choose $V$ so that the eigenvalues of $W$ and $V$ are typically of the same order. For a large class of diagonal matrices $V$ we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution $F_1$ in the limit of large $N$. Our proofs also apply to the complex Hermitian setting, i.e., when $W$ is a complex Hermitian Wigner matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-30T12:13:06.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-01T02:01:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60B20",
      "82B44"
    ],
    "keywords": [
      "deformed wigner matrices",
      "edge universality",
      "complex hermitian wigner matrix",
      "real symmetric wigner matrix",
      "assume subexponential decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8015O"
    }
  }
}