ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH

被引：25
作者：
Do, Yen [1 ]
Oanh Nguyen [2 ]
Vu, Van [3 ,4 ]
机构：
[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA
[2] Yale Univ, Dept Math, New Haven, CT 06520 USA
[3] Yale Univ, New Haven, CT 06520 USA
[4] Natl Univ Singapore, Dept Math, Level 4,Block S17,10 Lower Kent Ridge Rd, Singapore 119076, Singapore
来源：
ANNALS OF PROBABILITY | 2018年 / 46卷 / 05期
关键词：
Random polynomials; real roots; complex roots; correlation; arbitrary co-efficients; universality; REAL ZEROS; AVERAGE NUMBER; EXPECTED NUMBER; SERIES;
D O I：
10.1214/17-AOP1219
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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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页码：2407 / 2494
页数：88
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