{
  "id": "1806.08732",
  "version": "v1",
  "published": "2018-06-22T15:27:43.000Z",
  "updated": "2018-06-22T15:27:43.000Z",
  "title": "Level crossing in random matrices. II Random perturbation of a random matrix",
  "authors": [
    "Tobias Grøsfjeld",
    "Boris Shapiro",
    "Konstantin Zarembo"
  ],
  "comment": "27 pages, many figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "In this paper we study the distribution of level crossings for the spectra of linear families A+lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some generalisations. Besides, we present intriguing numerical information about the distribution of monodromy in case of linear families for the classical Gaussian ensembles of 3 * 3 matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-22T15:27:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix",
      "random perturbation",
      "level crossing",
      "classical gaussian ensembles",
      "linear families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}