Bose, Arup

Random circulant matrices - Florida CRC Press 2019 - xix, 192p. With index

Table of Contents

1. Circulants

2. Symmetric and reverse circulant

3. LSD: normal approximation

LSD: dependent input

Spectral radius: light tail

Spectral radius: k-circulant

Maximum of scaled eigenvalues: dependent input

Poisson convergence

Heavy tailed input: LSD

Heavy-tailed input: spectral radius


Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed.


Matrices -- Problems, exercises
Random matrices

512.9434 / B6R2

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