English

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 RR-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution.

Keywords

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