Convolution and Limit Theorems for Conditionally Free Random Variables
funct-an
2008-02-03 v1 Operator Algebras
Abstract
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its -transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution.
Cite
@article{arxiv.funct-an/9410004,
title = {Convolution and Limit Theorems for Conditionally Free Random Variables},
author = {Marek Bozejko and Michael Leinert and Roland Speicher},
journal= {arXiv preprint arXiv:funct-an/9410004},
year = {2008}
}
Comments
26 pages (pictures from R. Speicher), AMS-TeX 3.0, HD-AM-BLS-01