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A forest formula for pre-Lie exponentials, Magnus' operator and cumulant-cumulant relations
Adrian Celestino, Frédéric Patras
Forest formulas that generalize Zimmermann's forest formula in quantum field theory have been obtained for the computation of the antipode in the dual of enveloping algebras of pre…
Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants
Adrian Celestino, Kurusch Ebrahimi-Fard, Alexandru Nica +2
We consider the group of unitized multiplicative functions in the incidence algebra of non-crossing partitions, where ``'' denotes the convolution operation. W…
Relations between infinitesimal non-commutative cumulants
Adrian Celestino, Kurusch Ebrahimi-Fard, Daniel Perales
Boolean, free and monotone cumulants as well as relations among them, have proven to be important in the study of non-commutative probability theory. Quite notably, Boolean cumulan…