{
  "id": "2203.01861",
  "version": "v1",
  "published": "2022-03-03T17:16:13.000Z",
  "updated": "2022-03-03T17:16:13.000Z",
  "title": "Rank-uniform local law for Wigner matrices",
  "authors": [
    "Giorgio Cipolloni",
    "László Erdős",
    "Dominik Schröder"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the well-known averaged and isotropic local laws. As an application, we prove that the quadratic forms of a general deterministic matrix $A$ on the bulk eigenvectors of a Wigner matrix has approximately Gaussian fluctuation. For the bulk spectrum, we thus generalize our previous result \\cite{2103.06730} valid for test matrices $A$ of large rank as well as the result of Benigni and Lopatto \\cite{2103.12013} valid for specific small rank observables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-03T17:16:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52"
    ],
    "keywords": [
      "wigner matrix",
      "rank-uniform local law",
      "specific small rank observables",
      "isotropic local laws",
      "general deterministic matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}