Séminaire Lotharingien de Combinatoire, 78B.58 (2017), 12 pp.
Frédéric Menous, Jean-Christophe Novelli and Jean-Yves Thibon
Noncommutative Free Cumulants
The relation between moments and free cumulants in free probability is
essentially a compositional inversion. We lift it at the level of the
noncommutative Faà di Bruno algebra, and of an operad of Schröder
trees. We get a new formula for free cumulants in terms of trees, and
we recover an interpretation of the relation in terms of characters
due to Ebrahimi-Fard and Patras.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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