2 papers
math.PR2026
Pólya--Schur problems and free probability
Andrew Campbell, Jonas Jalowy
In this work, we build a bridge between the Pólya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the Pólya--Benz Theorem, classifying a c…
math.PR2026
Universality for roots of derivatives of entire functions via finite free probability
Andrew Campbell, Sean O'Rourke, David Renfrew
A universality conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789--3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] asserts that, under some…