Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems
Combinatorics
2012-12-06 v3 Operator Algebras
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.
Cite
@article{arxiv.math/0210442,
title = {Cumulants in noncommutative probability I. Noncommutative Exchangeability Systems},
author = {Franz Lehner},
journal= {arXiv preprint arXiv:math/0210442},
year = {2012}
}
Comments
30 pages, AMS-LaTeX; a few minor corrections