Daniel Perales Anaya

Postdoctoral Research Associate

Education

Ph.D., University of Waterloo, 2022.

M.S. (Probability and Statistics), Centro de Investigación en Matemáticas (CIMAT), 2018

B.S., Universidad Nacional Autónoma de México (UNAM), 2016

Research Groups

Analysis and Partial Differential Equations, Discrete Math, Operations Research, and Probability

Research Area

Finite Free Probability

Bio

Research Interests:

My research is in Finite Free Probability: a new topic that lies in the intersection between free probability, roots of polynomials, random matrices and combinatorics. I also enjoy working with non-commutative probability, infinitesimal freeness, random matrices, set partitions, cumulants and the free anticommutator.

Selected Publications: 

• A. Martínez-Finkelshtein, R. Morales, D. Perales. Zeros of orthogonal little q-Jacobi polynomials: interlacing and
  monotonicity. Preprint arXiv:2506.05492.
• O. Arizmendi, D. Perales, J. Vazquez-Becerra. Finite Free Convolution: Infinitesimal Distributions.
  Preprint arXiv:2505.01705.
• J. Campbell, R. Morales, D. Perales. Even Hypergeometric Polynomials and Finite Free Commutators.
  Preprint arXiv:2502.00254.
• O. Arizmendi, K. Fujie, D. Perales, Y. Ueda. 𝑆-transform in Finite Free Probability. Preprint arXiv:2408.09337.
• A. Martínez-Finkelshtein, R. Morales, D. Perales. Zeros of generalized hypergeometric polynomials via finite free convolution. Applications to multiple orthogonality. Constructive Approximation, 2025.