FLUCTUATIONS OF THE NUMBER OF CRITICAL POINTS OF RANDOM TRIGONOMETRIC POLYNOMIALS

被引：0

作者：

Nicolaescu, Liviu I. ^{[1
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

ANALELE STIINTIFICE ALE UNIVERSITATII AL I CUZA DIN IASI-SERIE NOUA-MATEMATICA | 2013年 / 59卷 / 01期

关键词：

random functions; critical points; Kac-Rice formula; ZEROS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Denote by Z(nu) the number of critical points of a random trigonometric polynomial of degree <= nu. We prove that as nu -> infinity the expectation of Z(nu) is asymptotic to 2 nu root 3/5 while its variance is asymptotic to delta(infinity)nu where delta(infinity) approximate to 0.35.

引用

页码：1 / 24

页数：24

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