Combinatorics of free cumulants

Details Combinatorics of free cumulants Combinatorics of free cumulants

1999-05-17

arxiv.org/abs/math/9905094v1

Mathematics

Combinatorics

26 pages, Latex2e

Scientific paper

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.

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