46 citations · 128 across the 37 of their papers we have counts for
25 papers · 1 filter
Free multiplicative convolution with an arbitrary measure on the real line
Octavio Arizmendi, Takahiro Hasebe, Yu Kitagawa
We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construc…
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
Central limit theorem for crossings in randomly embedded graphs
Santiago Arenas-Velilla, Octavio Arizmendi, J. E. Paguyo
We consider the number of crossings in a random embedding of a graph, , with vertices in convex position. We give explicit formulas for the mean and variance of the number of cr…
New combinatorial identity for the set of partitions and limit theorems in finite free probability theory
Octavio Arizmendi, Katsunori Fujie, Yuki Ueda
We provide a refined combinatorial identity for the set of partitions of , which plays an important role in investigating several limit theorems related to finite f…
Quantitative Estimates for Operator-Valued and Infinitesimal Boolean and Monotone Limit Theorems
Octavio Arizmendi, Marwa Banna, Pei-Lun Tseng
We provide Berry-Esseen bounds for sums of operator-valued Boolean and monotone independent variables, in terms of the first moments of the summands. Our bounds are on the level of…
Convergence Rate for The Number of Crossing in a Random Labelled Tree
Santiago Arenas-Velilla, Octavio Arizmendi
We consider the number of crossings in a random labelled tree with vertices in convex position. We give a new proof of the fact that this quantity is asymptotically Gaussian with m…
Cyclic independence: Boolean and monotone
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy ca…
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.
On a Berry-Esseen type limit theorem for Boolean convolution
Mauricio Salazar
We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures of finite sixth moment. The main tool is a quantitative version of the Stie…
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…
On the number of crossings in a random labelled tree with vertices in convex position
Octavio Arizmendi, Pilar Cano, Clemens Huemer
We prove that the number of crossings in a random labelled tree with vertices in convex position is asymptotically Gaussian with mean and variance . A similar res…
Limit theorems for free Lévy processes
Octavio Arizmendi, Takahiro Hasebe
We consider different limit theorems for additive and multiplicative free Lévy processes. The main results are concerned with positive and unitary multiplicative free Lévy processe…
A Berry Esseen type limit theorem for Boolean convolution
Octavio Arizmendi, Mauricio Salazar
We give estimates on the rate of convergence in the Boolean central limit theorem for the Lévy distance. In the case of measures with bounded support we obtain a sharp estimate by…
The exponential map in non-commutative probability
Michael Anshelevich, Octavio Arizmendi
The wrapping transformation is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measu…
On the asymptotic distribution of block-modified random matrices
Octavio Arizmendi, Ion Nechita, Carlos Vargas
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild ass…
Asymptotic spectral distributions of distance -graphs of star product graphs
Octavio Arizmendi, Tulio Gaxiola
Let be a finite connected graph and let be the distance -graph of the -fold star power of . For a fixed , we show that the large limit of…
Free Subordination and Belinschi-Nica Semigroup
Octavio Arizmendi, Takahiro Hasebe
We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with res…
Convergence of the Fourth Moment and Infinite Divisibility: Quantitative estimates
Octavio Arizmendi, Arturo Jaramillo
We give an estimate for the Kolmogorov distance between an infinitely divisible distribution (with mean zero and variance one) and the standard Gaussian distribution in terms of th…
Convergence of the Fourth Moment and Infinite Divisibility
Octavio Arizmendi
In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our result…
Free Infinite Divisibility for Ultrasphericals
Octavio Arizmendi, Serban T. Belinschi
We prove that the integral powers of the semicircular distribution are freely infinitely divisible. As a byproduct we get another proof of the free infnite divisibility of the clas…
Classical and free infinite divisibility for Boolean stable laws
Octavio Arizmendi, Takahiro Hasebe
We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index and an asymmetry coefficient . We prove that the…
k-Divisible random variables in free probability
Octavio Arizmendi
We introduce and study the notion of k-divisible elements in a non-commutative probability space. A k-divisible element is a (non-commutative) random variable whose n-th moment van…
On the Law of Free Subordinators
Octavio Arizmendi, Takahiro Hasebe, Noriyoshi Sakuma
We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supp…
On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws
Octavio Arizmendi, Takahiro Hasebe
We consider a class of probability measures which have explicit Cauchy-Stieltjes transforms. This class includes a symmetric beta distribution, a free Poisson law and s…