46 citations · 128 across the 37 of their papers we have counts for
48 papers
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…
-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
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…
On the -Schatten Energy of Bipartite Graphs
Octavio Arizmendi, José Guerrero
We give a Coulson integral formula and a Coulson-Jacobs formula for the -Schatten energy. We use this formulas to compare the -Schatten energy of different trees by using a q…
Crossings in Randomly Embedded Graphs
Santiago Arenas-Velilla, Octavio Arizmendi
We consider the number of crossings in a graph which is embedded randomly on a convex set of points. We give an estimate to the normal distribution in Kolmogorov distance which imp…
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.
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…
Universality of free random variables: atoms for non-commutative rational functions
Octavio Arizmendi, Guillaume Cébron, Roland Speicher +1
Consider a tuple of normal operators in a tracial operator algebra setting with prescribed sizes of the eigenspaces for each . We address the question what o…
Energy and Randic index of directed graphs
Gerardo Arizmendi, Octavio Arizmendi
The concept of Randic index has been extended recently for a digraph. We prove that , where is a digraph, and denotes the…
Graphs of Maximal Energy with Fixed Maximal Degree
Octavio Arizmendi, Jorge Fernandez Hidalgo
We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is -regular we obtain the bou…
The graph energy game
Gerardo Arizmendi, Octavio Arizmendi
We study the graph energy from a cooperative game viewpoint. We introduce \emph{the graph energy game} and show various properties. In particular, we see that it is a superadditive…
Barabasi-Albert trees are hypoenergetic
Octavio Arizmendi, Emilio Dominguez
We prove that graphs following the model of Barabasi-Albert tree with n vertices are hypoenergetic in the large n limit.
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…
Energy of a graph and Randic index
Gerardo Arizmendi, Octavio Arizmendi
We prove that, for any graph , its graph energy is at least twice the Randic index. We show that equality holds if and only if is the union of complete bipartite graphs.
Second Order Cumulants: second order even elements and R-diagonal elements
Octavio Arizmendi, James A. Mingo
We introduce -diagonal and even operators of second order. We give a formula for the second order free cumulants of the square of a second order even element in terms of t…
The Cyclic Group and the Transpose of an R-cyclic matrix
Octavio Arizmendi, James A. Mingo
We show that using the cyclic group the transpose of an R-cyclic matrix can be decomposed along diagonal parts into a sum of parts which are freely independent over diagonal scalar…
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…
Conditionally Free Reduced Products of Hilbert Spaces
Octavio Arizmendi, Miguel Ballesteros, Francisco Torres-Ayala
We present a product of pairs of pointed Hilbert spaces that, in the context of Bozėjko, Leinert and Speicher's theory of conditionally free probability, plays the role of the redu…