The zeros of random polynomials cluster uniformly near the unit circle

By C. Hughes, Ashkan Nikeghbali. Compositio Mathematica, 2004

107 citations recorded by the source corpus.

Abstract In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdős and Turan. More precisely, given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. The method we use is deterministic: in particular, we do not assume independence or equidistribution of the coefficients of the polynomial.

Subfields: Applied Mathematics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ce5a29a48a81fe65f7d79bc9c865235ff1208004

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Zakhar Kabluchko
2. Dmitry Zaporozhets

In Geometry and Topology

1. Zakhar Kabluchko
2. Dmitry Zaporozhets

In Statistics and Probability

1. Zakhar Kabluchko
2. Martin Schlather

Citations in the corpus

• Asymptotic distribution of complex zeros of random analytic functions (2014, background): “2 can be deduced from the result of Hughes and Nikeghbali [14] (which is partially based on the Erdős–Turan inequality).”