{
  "id": "1603.03307",
  "version": "v1",
  "published": "2016-03-10T15:50:40.000Z",
  "updated": "2016-03-10T15:50:40.000Z",
  "title": "Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix",
  "authors": [
    "B. Shapiro",
    "K. Zarembo"
  ],
  "comment": "30 pages, 13 figures",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We consider level crossing in a matrix family $H=H_0+\\lambda V$ where $H_0$ is a fixed $N\\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of $\\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-10T15:50:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random perturbation",
      "fixed matrix",
      "standard gaussian random matrix ensembles",
      "probability distribution",
      "approximate formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1427056
    }
  }
}