THE DISTRIBUTION OF THE ZEROS OF RANDOM TRIGONOMETRIC POLYNOMIALS

被引：38

作者：

Granville, Andrew ^{[1
]}

Wigman, Igor ^{[2
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[2] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2011年 / 133卷 / 02期

关键词：

CENTRAL-LIMIT-THEOREM; STATIONARY GAUSSIAN PROCESS; DEPENDENT RANDOM-VARIABLES; REAL ROOTS; NUMBER; LEVEL;

D O I：

10.1353/ajm.2011.0015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic distribution of the number Z(N) of zeros of random trigonometric polynomials of degree N as N -> infinity. It is known that as N grows to infinity, the expected number of the zeros is asymptotic to 2/root 3 . N. The asymptotic form of the variance was predicted by Bogomolny, Bohigas and Leboeuf to be cN for some c > 0. We prove that Z(N)-EZ(N)/root(C)N converges to the standard Gaussian. In addition, we find that the analogous result is applicable for the number of zeros in short intervals.

引用

页码：295 / 357

页数：63

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