Roots of random polynomials with coefficients of polynomial growth

Yen Do; Oanh Nguyen; Van Vu

doi:10.1214/17-AOP1219

Roots of random polynomials with coefficients of polynomial growth

Yen Do, Oanh Nguyen, Van Vu

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2407-2494
Number of pages	88
Journal	Annals of Probability
Volume	46
Issue number	5
DOIs	https://doi.org/10.1214/17-AOP1219
State	Published - Sep 1 2018

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Arbitrary coefficients
Complex roots
Correlation
Random polynomials
Real roots
Universality

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AU - Nguyen, Oanh

AU - Vu, Van

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2018.

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N2 - 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.

AB - 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.

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KW - Complex roots

KW - Correlation

KW - Random polynomials

KW - Real roots

KW - Universality

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ER -

Roots of random polynomials with coefficients of polynomial growth

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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