| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 5775398 | Advances in Applied Mathematics | 2017 | 28 Pages |
Abstract
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Faà di Bruno algebra, and then to the group of a free operad over Schröder trees. This leads to new combinatorial expressions, which remain valid for operator-valued free probability. Specializations of these expressions give back Speicher's formula in terms of noncrossing partitions, and its interpretation in terms of characters due to Ebrahimi-Fard and Patras.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Matthieu Josuat-Vergès, Frédéric Menous, Jean-Christophe Novelli, Jean-Yves Thibon,