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Article Dans Une Revue Infinite Dimensional Analysis, Quantum Probability and Related Topics Année : 2018

∆-cumulants in terms of moments

Résumé

The ∆-convolution of real probability measures, introduced by Bo˙ zejko, generalizes both free and boolean convolutions. It is linearized by the ∆-cumulants, and Yoshida gave a combinatorial formula for moments in terms of ∆-cumulants, that implicitly defines the latter. It relies on the definition of an appropriate weight on noncrossing partitions. We give here two different expressions for the ∆-cumulants: the first one is a simple variant of Lagrange inversion formula, and the second one is a combinatorial inversion of Yoshida's formula involving Schröder trees.
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Dates et versions

hal-02106470 , version 1 (23-04-2019)

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Matthieu Josuat-Vergès. ∆-cumulants in terms of moments. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2018, 21 (2), pp.Article ID 1850012. ⟨10.1142/S0219025718500121⟩. ⟨hal-02106470⟩
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