{
  "id": "1610.04101",
  "version": "v1",
  "published": "2016-10-13T14:34:43.000Z",
  "updated": "2016-10-13T14:34:43.000Z",
  "title": "Matrix liberation process I: Large deviation upper bound and almost sure convergence",
  "authors": [
    "Yoshimichi Ueda"
  ],
  "comment": "31 pages",
  "categories": [
    "math.PR",
    "math.OA"
  ],
  "abstract": "We introduce the concept of matrix liberation process, a random matrix counterpart of the liberation process in free probability, and prove a large deviation upper bound for its empirical distribution with several properties on its rate function. As a simple consequence we obtain the almost sure convergence of the empirical distribution of the matrix liberation process to that of the corresponding liberation process as continuous processes in large $N$ limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T14:34:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation upper bound",
      "matrix liberation process",
      "sure convergence",
      "random matrix counterpart",
      "empirical distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}