{
  "id": "1711.07420",
  "version": "v1",
  "published": "2017-11-20T17:21:28.000Z",
  "updated": "2017-11-20T17:21:28.000Z",
  "title": "Outliers in the spectrum for products of independent random matrices",
  "authors": [
    "Natalie Coston",
    "Sean O'Rourke",
    "Philip Matchett Wood"
  ],
  "comment": "61 pages, 9 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical distribution of the eigenvalues is described by the m-th power of the circular law. Moreover, this same limiting distribution continues to hold if each iid random matrix is additively perturbed by a bounded rank deterministic error. However, the bounded rank perturbations may create one or more outlier eigenvalues. We describe the asymptotic location of the outlier eigenvalues, which extends a result of Terence Tao for the case of a single iid matrix. Our methods also allow us to consider several other types of perturbations, including multiplicative perturbations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-20T17:21:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "independent random matrices",
      "outlier eigenvalues",
      "bounded rank deterministic error",
      "iid random matrix",
      "single iid matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}