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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…
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 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…