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Communication Dans Un Congrès Année : 2017

Noncommutative free cumulants

Résumé

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.
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Dates et versions

hal-04227636 , version 1 (03-10-2023)

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  • HAL Id : hal-04227636 , version 1

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Matthieu Josuat-Vergès, Frédéric Menous, Jean-Christophe Novelli, Jean-Yves Thibon. Noncommutative free cumulants. Formal Power Series and Algebraic Combinatorics, Jul 2017, London, United Kingdom. pp.Article #58. ⟨hal-04227636⟩
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