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September 2018 Roots of random polynomials with coefficients of polynomial growth
Yen Do, Oanh Nguyen, Van Vu
Ann. Probab. 46(5): 2407-2494 (September 2018). DOI: 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.

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Yen Do. Oanh Nguyen. Van Vu. "Roots of random polynomials with coefficients of polynomial growth." Ann. Probab. 46 (5) 2407 - 2494, September 2018. https://doi.org/10.1214/17-AOP1219

Information

Received: 1 May 2016; Revised: 1 July 2017; Published: September 2018
First available in Project Euclid: 24 August 2018

zbMATH: 06964341
MathSciNet: MR3846831
Digital Object Identifier: 10.1214/17-AOP1219

Subjects:
Primary: 60K35

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 5 • September 2018
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