Mathematische Zeitschrift

, Volume 248, Issue 1, pp 67–100

Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems



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 and various q-cumulants.


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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institut für Mathematik CTechnische Universität GrazGrazAustria

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