{
  "id": "math/0210442",
  "version": "v3",
  "published": "2002-10-29T14:24:12.000Z",
  "updated": "2004-09-02T10:46:02.000Z",
  "title": "Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems",
  "authors": [
    "Franz Lehner"
  ],
  "comment": "30 pages, AMS-LaTeX; a few minor corrections",
  "journal": "Math. Z. 248 (2004), 67--100",
  "doi": "10.1007/s00209-004-0653-0",
  "categories": [
    "math.CO",
    "math.OA"
  ],
  "abstract": "Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the formula says that cumulants are moments of a certain ``discrete Fourier transform'' of a random variable. This provides a simple unified method to understand the known examples of cumulants, like classical, free cumulants and various q-cumulants.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-09-02T10:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L53",
      "05A18"
    ],
    "keywords": [
      "noncommutative exchangeability systems",
      "noncommutative probability",
      "discrete fourier transform",
      "free cumulants",
      "essential property"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10442L"
    }
  }
}