{
  "id": "2109.01464",
  "version": "v1",
  "published": "2021-09-03T11:53:36.000Z",
  "updated": "2021-09-03T11:53:36.000Z",
  "title": "Limiting Spectral Distributions of Families of Block Matrix Ensembles",
  "authors": [
    "Teresa Dunn",
    "Henry L. Fleischmann",
    "Faye Jackson",
    "Simran Khunger",
    "Steven J. Miller",
    "Luke Reifenberg",
    "Alexander Shashkov",
    "Stephen Willis"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a new matrix operation on a pair of matrices, $\\text{swirl}(A,X),$ and discuss its implications on the limiting spectral distribution. In a special case, the resultant ensemble converges almost surely to the Rayleigh distribution. In proving this, we provide a novel combinatorial proof that the random matrix ensemble of circulant Hankel matrices converges almost surely to the Rayleigh distribution, using the method of moments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-03T11:53:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60B10"
    ],
    "keywords": [
      "limiting spectral distribution",
      "block matrix ensembles",
      "circulant hankel matrices converges",
      "rayleigh distribution",
      "novel combinatorial proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}