The Annals of Probability

Roots of random polynomials with coefficients of polynomial growth

Yen Do, Oanh Nguyen, and Van Vu

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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.

Article information

Source
Ann. Probab., Volume 46, Number 5 (2018), 2407-2494.

Dates
Received: May 2016
Revised: July 2017
First available in Project Euclid: 24 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1535097632

Digital Object Identifier
doi:10.1214/17-AOP1219

Mathematical Reviews number (MathSciNet)
MR3846831

Zentralblatt MATH identifier
06964341

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Random polynomials real roots complex roots correlation arbitrary coefficients universality

Citation

Do, Yen; Nguyen, Oanh; Vu, Van. Roots of random polynomials with coefficients of polynomial growth. Ann. Probab. 46 (2018), no. 5, 2407--2494. doi:10.1214/17-AOP1219. https://projecteuclid.org/euclid.aop/1535097632


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