{
  "id": "1505.02511",
  "version": "v1",
  "published": "2015-05-11T07:55:47.000Z",
  "updated": "2015-05-11T07:55:47.000Z",
  "title": "Dynamical correlation functions for products of random matrices",
  "authors": [
    "Eugene Strahov"
  ],
  "comment": "27 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in the random matrix product plays a role of a discrete time. We consider in detail the case when the (squared) singular values of the initial random matrix form a polynomial ensemble, and the initial random matrix is multiplied by standard complex Gaussian matrices. In this case we show that the random process is a discrete-time determinantal point process. For three special cases (the case when the initial random matrix is a standard complex Gaussian matrix, the case when it is a truncated unitary matrix, or the case when it is a standard complex Gaussian matrix with a source) we compute the dynamical correlations functions explicitly, and find the hard edge scaling limits of the correlation kernels. The proofs rely on the Eynard-Mehta theorem, and on contour integral representations for the correlation kernels suitable for an asymptotic analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-11T07:55:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "standard complex gaussian matrix",
      "dynamical correlation functions",
      "random process",
      "correlation kernels",
      "random matrix product plays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502511S"
    }
  }
}