Work

Zeros and Exponential Profiles of Polynomials II: Examples

Year: 2026

Type: article

Abstract: In [Jalowy, Kabluchko, Marynych, Part I of the present work, Constr. Approx.], the authors discuss a user-friendly approach to determine the limiting empirical zero distribution of a sequence of real-rooted polynomials, as the degree goes to $$\infty $$ ∞ . In this note, we aim to apply it to a vast range of examples of polynomials providing a unifying source for limiting empirical zero distributions. We cover Touchard, Fubini, Eulerian, Narayana and little q -Laguerre polynomials as well as hypergeometric polynomials including the classical Hermite, Laguerre and Jacobi polynomials. We construct polynomials whose empirical zero distributions converge to the free multiplicative normal and Poisson distributions. Furthermore, we study polynomials generated by some differential operators. As one inverse result, we derive coefficient asymptotics of the characteristic polynomial of random covariance matrices.

Source: Constructive Approximation

DOI: 10.1007/s00365-026-09775-2

Authors: Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych

Institutions: Paderborn University, University of Münster, Kyiv School of Economics

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Deutsche Forschungsgemeinschaft