{
  "id": "1611.07440",
  "version": "v1",
  "published": "2016-11-22T17:58:05.000Z",
  "updated": "2016-11-22T17:58:05.000Z",
  "title": "Spectral properties of polynomials in independent Wigner and deterministic matrices",
  "authors": [
    "Serban Belinschi",
    "Mireille Capitaine"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic probability measures, which is computed with the tools of free probability. On the other hand, we establish the strong asymptotic freeness of independent Wigner matrices and any family of deterministic matrices with strong limiting distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-22T17:58:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "15B52",
      "60B20",
      "46L54"
    ],
    "keywords": [
      "deterministic matrices",
      "spectral properties",
      "deterministic probability measures",
      "strong asymptotic freeness",
      "independent wigner matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}