Combinatorics of free cumulants
Combinatorics
2007-05-23 v1 Operator Algebras
Probability
Abstract
We derive a formula for expressing free cumulants whose entries are products of random variables in terms of the lattice structure of non-crossing partitions. We show the usefulness of that result by giving direct and conceptually simple proofs for a lot of results about -diagonal elements. Our investigations do not assume the trace property for the considered linear functionals.
Cite
@article{arxiv.math/9905094,
title = {Combinatorics of free cumulants},
author = {Bernadette Krawczyk and Roland Speicher},
journal= {arXiv preprint arXiv:math/9905094},
year = {2007}
}
Comments
26 pages, Latex2e