8 papers
Repeated differentiation of deterministic polynomials with asymptotically radial root distributions
Brian C. Hall, Daniel Perales
Recent works of Galligo, Najnudel, and Vu (2025) and Najnudel and Vu (2026) study repeated differentiation for polynomials of the form , where is a deterministic p…
Multiplicative and Additive Finite Free Convolutions for q-Polynomials
Andrei Martinez-Finkelshtein, Daniel Perales, Rafael Morales
We study -analogs of finite free convolutions and their interaction with families of -hypergeometric polynomials. First, we revisit the -multiplicative finite free convolu…
Asymptotic root distribution of polynomials under repeated polar differentiation
Daniel Perales, Zhiyuan Yang
Given a sequence of real rooted polynomials with a fixed asymptotic root distribution, we study the asymptotic root distribution of the repeated polar derivativ…
Second order free cumulants: product, commutator, and anti-commutator
Daniel Munoz George, Daniel Perales
Given two second order free random variables and , we study the second order free cumulants of their product , their commutator , and their anti-commutator $ab+ba…
Zeros of orthogonal little q-Jacobi polynomials: interlacing and monotonicity
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
We investigate the distribution of zeros of the little q-Jacobi polynomials and related q-hypergeometric families. We prove that the zeros of these orthogonal polynomials exhibit s…
Even Hypergeometric Polynomials and Finite Free Commutators
Jacob Campbell, Rafael Morales, Daniel Perales
We study in detail the class of even polynomials and their behavior with respect to finite free convolutions. To this end, we use some specific hypergeometric polynomials and a var…
Zeros of generalized hypergeometric polynomials via finite free convolution. Applications to multiple orthogonality
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
We address the problem of the weak asymptotic behavior of zeros of families of generalized hypergeometric polynomials as their degree tends to infinity. The main tool is the repres…
Real roots of hypergeometric polynomials via finite free convolution
Andrei Martinez-Finkelshtein, Rafael Morales, Daniel Perales
We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric p…