{
  "id": "1207.3831",
  "version": "v2",
  "published": "2012-07-16T21:58:13.000Z",
  "updated": "2012-12-14T16:52:47.000Z",
  "title": "Covariation representations for Hermitian Lévy process ensembles of free infinitely divisible distributions",
  "authors": [
    "J. Armando Domínguez-Molina",
    "Víctor Pérez-Abreu",
    "Alfonso Rocha-Arteaga"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles $(M_{d})_{d\\geq1}$ whose asymptotic spectral distributions are free infinitely divisible. We investigate Hermitian L\\'{e}vy processes with jumps of rank one associated to these random matrix ensembles introduced in [6] and [10]. A sample path approximation by covariation processes for these matrix L\\'{e}vy processes is obtained. As a general result we prove that any $d\\times d$ complex matrix subordinator with jumps of rank one is the quadratic variation of an $\\mathbb{C}^{d}$-valued L\\'{e}vy process. In particular, we have the corresponding result for matrix subordinators with jumps of rank one associated to the random matrix ensembles $(M_{d})_{d\\geq1}$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-14T16:52:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60E07",
      "60G51",
      "60G57"
    ],
    "keywords": [
      "hermitian lévy process ensembles",
      "free infinitely divisible distributions",
      "random matrix ensembles",
      "covariation representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3831D"
    }
  }
}