5 citations · 8 across the 7 of their papers we have counts for
7 papers
Conditionally monotone cumulants via shuffle algebra
Adrian Celestino, Kurusch Ebrahimi-Fard
In this work we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as…
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…
Monotone Cumulant-Moment Formula and Schröder Trees
Octavio Arizmendi, Adrian Celestino
We prove a formula to express multivariate monotone cumulants of random variables in terms of their moments by using a Hopf algebra of decorated Schröder trees.
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…
Cumulant-cumulant relations in free probability theory from Magnus' expansion
A. Celestino, K. Ebrahimi-Fard, F. Patras +1
Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants c…
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…
Polynomials on cyclic monotone elements with applications to random matrices with discrete spectrum
Octavio Arizmendi, Adrian Celestino
We provide a generalization and new proofs of the formulas of Collins, Hasebe and Sakuma for the spectrum of polynomials in cyclic monotone elements. This is applied to random matr…