On the number of real roots of random polynomials-Reference-Cited by-同舟云学术

On the number of real roots of random polynomials

Published:2016-05-03 Issue:04 Volume:18 Page:1550052
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Nguyen Hoi¹,Nguyen Oanh²,Vu Van²

Affiliation:

1. Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA

2. Department of Mathematics, Yale University, New Haven, CT 06520, USA

Abstract

Roots of random polynomials have been studied intensively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdős–Offord, showed that the expectation of the number of real roots is [Formula: see text]. In this paper, we determine the true nature of the error term by showing that the expectation equals [Formula: see text]. Prior to this paper, the error term [Formula: see text] has been known only for polynomials with Gaussian coefficients.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199715500522

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