Concentration of the number of real roots of random polynomials

Abstract

Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some extent. Our method is elementary and works well for many models of random polynomials, with gaussian or non-gaussian coefficients.

arXiv admin note: text overlap with arXiv:2008.04111, arXiv:1912.12051