{
  "id": "1906.10268",
  "version": "v1",
  "published": "2019-06-24T23:47:25.000Z",
  "updated": "2019-06-24T23:47:25.000Z",
  "title": "Finite-rank perturbations of random band matrices via infinitesimal free probability",
  "authors": [
    "Benson Au"
  ],
  "comment": "34 pages, 5 figures",
  "categories": [
    "math.PR",
    "math.OA"
  ],
  "abstract": "We prove a sharp $\\sqrt{N}$ transition for the infinitesimal distribution of a periodically banded GUE matrix. For band widths $b_N = \\Omega(\\sqrt{N})$, we further prove that our model is infinitesimally free from the matrix units and the normalized all-ones matrix. Our results allow us to extend previous work of Shlyakhtenko on finite-rank perturbations of Wigner matrices in the infinitesimal framework. For finite-rank perturbations of our model, we find outliers at the classical positions from the deformed Wigner ensemble.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-24T23:47:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B52",
      "46L53",
      "46L54",
      "60B20"
    ],
    "keywords": [
      "finite-rank perturbations",
      "random band matrices",
      "infinitesimal free probability",
      "wigner matrices",
      "infinitesimal distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}