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Combinatorics of Free Cumulants

✍ Scribed by Bernadette Krawczyk; Roland Speicher

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 282 KB
Volume: 90
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3032

No coin nor oath required. For personal study only.

✦ Synopsis

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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