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 $R$-diagonal elements.
Our investigations do not assume the trace property for the considered linear
functionals.
%0 Journal Article
%1 krawczyk1999combinatorics
%A Krawczyk, Bernadette
%A Speicher, Roland
%D 1999
%K combinatorics probability theory
%T Combinatorics of free cumulants
%U http://arxiv.org/abs/math/9905094
%X 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 $R$-diagonal elements.
Our investigations do not assume the trace property for the considered linear
functionals.
@article{krawczyk1999combinatorics,
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 $R$-diagonal elements.
Our investigations do not assume the trace property for the considered linear
functionals.},
added-at = {2020-02-06T15:19:57.000+0100},
author = {Krawczyk, Bernadette and Speicher, Roland},
biburl = {https://www.bibsonomy.org/bibtex/2cf2aecaa50d0b1ae39f711e6de96b9ad/kirk86},
description = {[math/9905094] Combinatorics of free cumulants},
interhash = {1d8c62696b7fb26d338441262d424c70},
intrahash = {cf2aecaa50d0b1ae39f711e6de96b9ad},
keywords = {combinatorics probability theory},
note = {cite arxiv:math/9905094Comment: 26 pages, Latex2e},
timestamp = {2020-02-06T15:20:36.000+0100},
title = {Combinatorics of free cumulants},
url = {http://arxiv.org/abs/math/9905094},
year = 1999
}