ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH

• 成果类型: Article
• 署名作者: Do, Yen; Oanh Nguyen; Vu, Van
• 署名单位: University of Virginia; Yale University; Yale University; National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1219
• 发表日期: 2018
• 页码: 2407-2494
• 关键词: real zeros; AVERAGE NUMBER; expected number; series

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.