{
  "id": "1710.08160",
  "version": "v1",
  "published": "2017-10-23T09:20:48.000Z",
  "updated": "2017-10-23T09:20:48.000Z",
  "title": "Brown measure and asymptotic freeness of elliptic and related matrices",
  "authors": [
    "Kartick Adhikari",
    "Arup Bose"
  ],
  "comment": "19 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that independent elliptic matrices converge to freely independent elliptic elements. Moreover, the elliptic matrices are asymptotically free with deterministic matrices under appropriate conditions. We compute the Brown measure of the product of elliptic elements. It turns out that this Brown measure is same as the limiting spectral distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-23T09:20:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F99"
    ],
    "keywords": [
      "brown measure",
      "asymptotic freeness",
      "related matrices",
      "independent elliptic matrices converge",
      "freely independent elliptic elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}