{
  "id": "1405.6634",
  "version": "v3",
  "published": "2014-05-26T16:37:11.000Z",
  "updated": "2016-06-07T05:51:09.000Z",
  "title": "Bulk universality for deformed Wigner matrices",
  "authors": [
    "Ji Oon Lee",
    "Kevin Schnelli",
    "Ben Stetler",
    "Horng-Tzer Yau"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/15-AOP1023 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2016, Vol. 44, No. 3, 2349-2425",
  "doi": "10.1214/15-AOP1023",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider $N\\times N$ random matrices of the form $H=W+V$ where $W$ is a real symmetric or complex Hermitian Wigner matrix and $V$ is 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 local statistics in the bulk of the spectrum are universal in the limit of large $N$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-30T12:22:08.000Z",
      "title": "Bulk Universality for Deformed Wigner Matrices",
      "abstract": "We consider $N\\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric or complex Hermitian Wigner matrix and $V$ a real, diagonal, random or deterministic 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 local statistics in the bulk of the spectrum are universal in the limit of large $N$.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-06-07T05:51:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "60B20",
      "82B44"
    ],
    "keywords": [
      "deformed wigner matrices",
      "bulk universality",
      "complex hermitian wigner matrix",
      "assume subexponential decay",
      "real symmetric"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6634O"
    }
  }
}