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4 papers
An analytic approach to the finite R-transform
Octavio Arizmendi, Katsunori Fujie
We revisit Marcus' finite free analogue of Voiculescu -transform from an analytic viewpoint. By relating the finite free Fourier transform to the Laplace transform, we study the…
Critical points of random polynomials and finite free cumulants
Octavio Arizmendi, Andrew Campbell, Katsunori Fujie
A result of Hoskins and Steinerberger [Int. Math. Res. Not., (13):9784-9809, 2022] states that repeatedly differentiating a random polynomials with independent and identically dist…
Finite Free Convolution: Infinitesimal Distributions
Octavio Arizmendi, Daniel Perales, Josue Vazquez-Becerra
Finite-free additive and multiplicative convolutions are operations on the set of polynomials with real roots, introduced independently by Szegö and Walsh in the 1920s. These opera…
BMT Independence
Octavio Arizmendi, Saul Rogelio Mendoza, Josué Vazquez-Becerra
We introduce the notion of BMT independence, allowing us to take arbitrary mixtures of boolean, monotone, and tensor independence and generalizing the notion of BM independence of…