Free convolution powers via roots of polynomials

S Steinerberger - Experimental Mathematics, 2023 - Taylor & Francis
Let μ be a compactly supported probability measure on the real line. Bercovici-Voiculescu
and Nica-Speicher proved the existence of a free convolution power μ⊞ k for any real k≥ 1 …

A semicircle law for derivatives of random polynomials

JG Hoskins, S Steinerberger - … Mathematics Research Notices, 2022 - academic.oup.com
Let be independent and identically distributed real-valued random variables with mean zero,
unit variance, and finite moments of all remaining orders. We study the random polynomial …

Sums of random polynomials with differing degrees

I Kraus, M Michelen, S O'Rourke - Transactions of the American …, 2024 - ams.org
Let $\mu $ and $\nu $ be probability measures in the complex plane, and let $ p $ and $ q $
be independent random polynomials of degree $ n $, whose roots are chosen …