Roots of random polynomials with coefficients having polynomial growth

Yen Do; Oanh Nguyen; Van Vu

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arXiv · 1507.04994

Roots of random polynomials with coefficients having polynomial growth

Yen Do·Oanh Nguyen·Van Vu

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Abstract

In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coeffcients 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 coeffcients 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. 2015-07-17. Roots of random polynomials with coefficients having polynomial growth. https://arxiv.org/abs/1507.04994

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