{
  "id": "1801.10512",
  "version": "v1",
  "published": "2018-01-31T15:52:21.000Z",
  "updated": "2018-01-31T15:52:21.000Z",
  "title": "Eigenvectors of a matrix under random perturbation",
  "authors": [
    "Florent Benaych-Georges",
    "Nathanaël Enriquez",
    "Alkéos Michaïl"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors 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, centered, with a variance profile. This is done through a perturbative expansion of spectral measures associated to the state defined by a given vector.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-31T15:52:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random perturbation",
      "perturbative expansion",
      "small operator norm",
      "spectral measures",
      "eigenvector basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}