3 citations · 5 across the 15 of their papers we have counts for
5 papers · 1 filter
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…