Combinatorics of free cumulants

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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.
26 pages, Latex2e

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Combinatorics, Operator Algebras, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/78508

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9905094
 http://arxiv.org/abs/math/9905094

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arXiv