Poisson convergence of eigenvalues of circulant type matrices

被引：10

作者：

Bose, Arup ^{[1
]}

Hazra, Rajat Subhra ^{[1
]}

Saha, Koushik ^{[1
]}

机构：

[1] Indian Stat Inst, Stat & Math Unit, Kolkata 700108, India

来源：

EXTREMES | 2011年 / 14卷 / 04期

关键词：

Circulant matrix; k-circulant matrix; Eigenvalues; Large dimensional random matrix; Moving average process; Normal approximation; Point process; Poisson random measure; Reverse circulant matrix; Spectral density; Symmetric circulant matrix; STATISTICS;

D O I：

10.1007/s10687-010-0115-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the point processes based on the eigenvalues of the reverse circulant, symmetric circulant and k-circulant matrices with i.i.d. entries and show that they converge to a Poisson random measures in vague topology. The joint convergence of upper ordered eigenvalues and their spacings follow from this. We extend these results partially to the situation where the entries are come from a two sided moving average process.

引用

页码：365 / 392

页数：28

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