Noncrossing linked partitions, the partial order on , and the transform
Author:
Alexandru Nica
Journal:
Proc. Amer. Math. Soc. 138 (2010), 12731285
MSC (2010):
Primary 46L54; Secondary 05A18
Published electronically:
December 1, 2009
MathSciNet review:
2578521
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Abstract: The paper establishes a connection between two recent combinatorial developments in free probability: the noncrossing linked partitions introduced by Dykema in 2007 to study the transform, and the partial order on introduced by Belinschi and Nica in 2008 in order to study relations between free and Boolean probability. More precisely, one has a canonical bijection between (the set of all noncrossing linked partitions of ) and the set . As a consequence of this bijection, one gets an alternative description of Dykema's formula expressing the moments of a noncommutative random variable in terms of the coefficients of the reciprocal transform . Moreover, due to the Boolean features of , this formula can be simplified to a form which resembles the momentcumulant formula from free probability.
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Additional Information
Alexandru Nica
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Email:
anica@math.uwaterloo.ca
DOI:
http://dx.doi.org/10.1090/S0002993909102186
PII:
S 00029939(09)102186
Received by editor(s):
January 29, 2009
Published electronically:
December 1, 2009
Additional Notes:
Research supported by a Discovery Grant from NSERC, Canada
Communicated by:
Marius Junge
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
