ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH

Do Yen; Oanh Nguyen; Vu Van

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ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH

机译：随机多项式与多项式生长系数的根

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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.

机译：在本文中，我们证明了具有多项式的随机多项式的根系的最佳局部普遍性。作为一个应用程序，我们首次推出了这些多项式的真实根数的尖锐估计，即使当系数没有明确时，也是如此。我们的结果还持有系列; 特别是，我们证明了随机双曲系列的本地普遍性。

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《The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics》 |2018年第5期|共88页
作者
Do Yen; Oanh Nguyen; Vu Van;
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作者单位

Univ Virginia Dept Math Charlottesville VA 22904 USA;

Yale Univ Dept Math New Haven CT 06520 USA;

Yale Univ New Haven CT 06520 USA;

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原文格式 PDF
正文语种 eng
中图分类概率论（几率论、或然率论）;
关键词
Random polynomials; real roots; complex roots; correlation; arbitrary co-efficients; universality;

机译：随机多项式;真实根;复杂根;相关性;任意合作;普遍性;

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专利

1. ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH [J] . Do Yen, Oanh Nguyen, Vu Van The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2018,第5期

机译：随机多项式与多项式生长系数的根
2. Algorithm for Calculating the Roots of Polynomials with Coefficients in the Ring of Polynomials over an Arbitrary Integral Domain [J] . A. E. Maevskii Mathematical notes . 2009,第1a2期

机译：任意整数域上具有多项式环中多项式的根的计算算法
3. Roots of random polynomials whose coefficients have logarithmic tails [J] . Kabluchko Z., Zaporozhets D. The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2013,第5期

机译：系数为对数尾的随机多项式的根
4. Insights on Asymptotic Behavior of Characteristic Roots of Quasi-Polynomials with Delay-Dependent Coefficients in Some Ill-Posed Cases [C] . A. Martinez-Gonzalez, C. F. Mendez-Barrios, S. I. Niculescu, IFAC Workshop on Time Delay Systems . 2020

机译：在一些不良病例中延迟依赖系数对准多项式特征根渐近行为的见解
5. On the Pairing Between Zeros and Critical Points of Random Polynomials With Independent Roots [D] . Williams, Noah. 2019

机译：具有独立根的随机多项式的零和临界点之间的配对
6. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials [O] . Paul Barry 2013

机译：Chebyshev-Boubaker多项式的连接系数
7. On the distribution of polynomials with bounded roots, I. Polynomials with real coefficients [O] . AKIYAMA Shigeki, PETHŐ Attila 2014

机译：关于有根的多项式的分布，I。实系数的多项式
8. NUMERICAL EVALUATION OF ROOTS OF A POLYNOMIAL WITH COMPLEX COEFFICIENTS [R] . Dan Wolfman 1969

机译：复杂系数多项式根的数值评估

ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH

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