{
  "id": "1706.06189",
  "version": "v1",
  "published": "2017-06-19T21:51:54.000Z",
  "updated": "2017-06-19T21:51:54.000Z",
  "title": "Spectral statistics for product matrix ensembles of Hermite type with external source",
  "authors": [
    "Dang-Zheng Liu"
  ],
  "comment": "Preliminary Version. Comments Welcome",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We continue investigating spectral properties of a Hermitised random matrix product, which, contrary to previous product ensembles, allows for eigenvalues on the full real line. When a GUE matrix with an external source is involved, we prove that the eigenvalues of the product form a determinantal point process and derive a double integral representation for correlation kernel. As the source changes, we observe a critical value and establish the existence of a phase transition for scaled eigenvalues at the origin. Particularly in the critical case, we obtain a new family of Pearcey-type kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-19T21:51:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20"
    ],
    "keywords": [
      "product matrix ensembles",
      "external source",
      "spectral statistics",
      "hermite type",
      "hermitised random matrix product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}