Persistence of random polynomials
Presenter
August 7, 2025
Abstract
We show that the probability that a random polynomial with iid coefficients and even degree has no real roots decays polynomially in the degree with a universal persistence exponent, as soon as the iid coefficients have mean zero and variance one. Our results apply to a broader class of polynomials, where the coefficients can be multiplied by a regularly varying function.
This talk is based on joint work with Promit Ghosal at University of Chicago.