Combinatorics of free cumulants

Authors
Krawczyk, B Speicher, R
Citation
B. Krawczyk et R. Speicher, Combinatorics of free cumulants, J COMB TH A, 90(2), 2000, pp. 267-292
Citations number
17
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
90
Issue
2
Year of publication
2000
Pages
267 - 292
Database
ISI
SICI code
0097-3165(200005)90:2<267:COFC>2.0.ZU;2-G
Abstract
We derive a formula for expressing free cumulants whose entries are product s of random variables in terms of the lattice structure of non-crossing par titions. We show the usefulness of that result by giving direct and concept ually simple proofs for a lot of results about R-diagonal elements. Our inv estigations do not assume the trace property for the considered linear func tionals. (C) 2000 Academic Press.