{
  "id": "1701.02597",
  "version": "v1",
  "published": "2017-01-10T14:03:39.000Z",
  "updated": "2017-01-10T14:03:39.000Z",
  "title": "Perturbations by random matrices",
  "authors": [
    "Florent Benaych-Georges",
    "Nathanaël Enriquez",
    "Alkéos Michaïl"
  ],
  "comment": "25 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent with a variance profile. We prove that, depending on the order of magnitude of the perturbation, several regimes can appear, called perturbative and semi-perturbative regimes. Depending on the regime, the leading terms of the expansion are either related to free probability theory or to the one-dimensional Gaussian free field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-10T14:03:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A52",
      "60B20",
      "47A55",
      "46L54"
    ],
    "keywords": [
      "random matrix",
      "perturbation",
      "one-dimensional gaussian free field",
      "small operator norm",
      "free probability theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}