{
  "id": "1711.07103",
  "version": "v1",
  "published": "2017-11-19T23:26:57.000Z",
  "updated": "2017-11-19T23:26:57.000Z",
  "title": "Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices",
  "authors": [
    "Lucas Benigni"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\\times N$ Rosenzweig-Porter model. We prove that the eigenvectors entries are asymptotically Gaussian with a specific variance, localizing them onto a small, explicit, part of the spectrum. For a well spread initial spectrum, this variance profile universally follows a heavy-tailed Cauchy distribution. The proof relies on a priori local laws for this model as given in [28, 27, 11] and the eigenvector moment flow from [12].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-19T23:26:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "15B52",
      "58J51"
    ],
    "keywords": [
      "quantum unique ergodicity",
      "deformed wigner matrices",
      "eigenvectors distribution",
      "spread initial spectrum",
      "priori local laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}