Roots of random polynomials with coefficients of polynomial growth

Yen Do, Hoi H. Nguyen, Van Vu

Type: Article

Publication Date: 2018-08-24

Citations: 32

DOI: https://doi.org/10.1214/17-aop1219

Abstract

In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coefficients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these polynomials, even when the coefficients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.

Locations

The Annals of Probability - View - PDF

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