5 citations · 14 across the 9 of their papers we have counts for
10 papers
Finite Free Convolution: Infinitesimal Distributions
Octavio Arizmendi, Daniel Perales, Josue Vazquez-Becerra
Finite-free additive and multiplicative convolutions are operations on the set of polynomials with real roots, introduced independently by Szegö and Walsh in the 1920s. These opera…
-transform in Finite Free Probability
Octavio Arizmendi, Katsunori Fujie, Daniel Perales +1
We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial b…
A Berry-Essen Type Theorem for Finite Free Convolution
Octavio Arizmendi, Daniel Perales
We prove that the rate of convergence for the central limit theorem in finite free convolution is of order
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…
On the anti-commutator of two free random variables
Daniel Perales
Let denote the sequence of free cumulants of a random variable in a non-commutative probability space . Based on some considerations on bi…
On operator-valued infinitesimal Boolean and monotone independence
Daniel Perales, Pei-Lun Tseng
We introduce the notion of operator-valued infinitesimal (OVI) independence for the Boolean and monotone cases. Then show that OVI Boolean (resp. monotone) independence is equivale…
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…
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…