5 citations · 14 across the 9 of their papers we have counts for
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Finite Free Cumulants: Multiplicative Convolutions, Genus Expansion and Infinitesimal Distributions
Octavio Arizmendi, Jorge Garza-Vargas, Daniel Perales
Given two polynomials of degree , we give a combinatorial formula for the finite free cumulants of . We show that this formula admits a topolo…
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…
Cumulants for finite free convolution
Octavio Arizmendi, Daniel Perales
In this paper we define cumulants for finite free convolution. We give a moment-cumulant formula and show that these cumulants satisfy desired properties: they are additive with re…