On distribution of zeros of random polynomials in complex plane

被引：0

作者：

Ibragimov, Ildar ^{[1
]}

Zaporozhets, Dmitry ^{[1
]}

机构：

[1] St. Petersburg Department of Steklov Mathematical Institute RAS, St. Petersburg, 191023

来源：

Springer Proceedings in Mathematics and Statistics | 2013年 / 33卷

基金：

俄罗斯基础研究基金会;

关键词：

Random analytic function; Roots concentration; Roots of random polynomial;

D O I：

10.1007/978-3-642-33549-5_18

中图分类号：

学科分类号：

摘要：

Let Gn(z)=ξ0 + ξ1z +...+ ξnzn be a random polynomial with i.i.d. coefficients (real or complex). We show that the arguments of the roots of Gn(z) are uniformly distributed in [0, 2π] asymptotically as n→∞. We also prove that the condition E ln(1 + {pipe}ξ0{pipe}<1∞ is necessary and sufficient for the roots to asymptotically concentrate near the unit circumference. © Springer-Verlag Berlin Heidelberg 2013.

引用

页码：303 / 323

页数：20

共 3 条

[1] ASYMPTOTIC DISTRIBUTION OF COMPLEX ZEROS OF RANDOM ANALYTIC FUNCTIONS
Kabluchko, Zakhar
Zaporozhets, Dmitry
ANNALS OF PROBABILITY, 2014, 42 (04) : 1374 - 1395
[2] ON THE DISTRIBUTION OF COMPLEX ROOTS OF RANDOM POLYNOMIALS WITH HEAVY-TAILED COEFFICIENTS
Goetze, F.
Zaporozhets, D.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2012, 56 (04) : 696 - U217
[3] THE ANGULAR DISTRIBUTION OF ZEROS OF RANDOM ANALYTIC FUNCTIONS
Mahola, M. P.
Filevych, P. V.
UFA MATHEMATICAL JOURNAL, 2012, 4 (01): : 115 - 127

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