{
  "id": "1810.00433",
  "version": "v1",
  "published": "2018-09-30T17:56:59.000Z",
  "updated": "2018-09-30T17:56:59.000Z",
  "title": "Lyapunov exponent, universality and phase transition for products of random matrices",
  "authors": [
    "Dang-Zheng Liu",
    "Dong Wang",
    "Yanhui Wang"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We are devoted to solving one problem, which is proposed by Akemann, Burda, Kieburg \\cite{ABK} and Deift \\cite{D17}, on local statistics of finite Lyapunov exponents for $M$ products of $N\\times N$ Gaussian random matrices as both $M$ and $N$ go to infinity. When the ratio $(M+1)/N$ changes from $0$ to $\\infty$, we prove that the local statistics undergoes a transition from GUE to Gaussian. Especially at the critical scaling $(M+1)/N \\to \\gamma \\in (0,\\infty)$, we observe a phase transition phenomenon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-30T17:56:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "universality",
      "finite lyapunov exponents",
      "gaussian random matrices",
      "local statistics undergoes",
      "phase transition phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}