46 citations · 62 across the 7 of their papers we have counts for
9 papers
Combinatorics of NC-Probability Spaces with Independent Constants
Carlos Dias-Aguilera, Tulio Gaxiola, Jorge Santos +1
Unlike classical and free independence, the boolean and monotone notions of independence lack of the property of independent constants. In the scalar case, this leads to restrictio…
Subordination methods for free deconvolution
Octavio Arizmendi, Pierre Tarrago, Carlos Vargas
In this paper, we give subordination functions for free additive and free multiplicative deconvolutions in some domain of the complex half-plane, under the condition that the distr…
Non-commutative Probability Theory for Topological Data Analysis
Carlos Vargas
Recent developments have found unexpected connections between non-commutative probability theory and algebraic topology. In particular, Boolean cumulants functionals seem to be imp…
A General Solution to (Free) Deterministic Equivalents
Carlos Vargas
We give an algorithm to compute the asymptotics of the eigenvalue distribution of quite general matricial central limit theorems. The central limits are the so called free determin…
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…
Relations between cumulants in noncommutative probability
Octavio Arizmendi, Takahiro Hasebe, Franz Lehner +1
We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determi…
Operator-valued free multiplicative convolution: analytic subordination theory and applications to random matrix theory
Serban T. Belinschi, Roland Speicher, John Treilhard +1
We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtai…
Products of free random variables and k-divisible partitions
Octavio Arizmendi, Carlos Vargas
We derive a formula for the moments and the free cumulants of the multiplication of free random variables in terms of -equal and -divisible non-crossing partitions. This…
Free Deterministic Equivalents, Rectangular Random Matrix Models, and Operator-Valued Free Probability Theory
Roland Speicher, Carlos Vargas, Tobias Mai
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random m…