Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability
Year: 2026
Type: preprint
Abstract: The asymptotic behavior of the coefficients of a sequence of polynomials is given under the conditions that all the zeros are real and positive and the zeros have an asymptotic zero distribution on $(0,\infty)$. We show how the limit for the coefficients is related to the Stieltjes transform of the asymptotic zero distribution and make a connection with the $S$-transform in free probability. We illustrate with some examples involving orthogonal and multiple orthogonal polynomials.
Source: arXiv (Cornell University)
Author: Van Assche, Walter
Institution: KU Leuven
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212527028