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Random circulant matrices

By: Bose, Arup.
Contributor(s): Saha, Koushik [Co author].
Material type: materialTypeLabelBookPublisher: Florida CRC Press 2019Description: xix, 192p. With index.ISBN: 9781138351097.Subject(s): Matrices -- Problems, exercises | Random matrices | EigenvaluesDDC classification: 512.9434 Summary: 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. https://www.crcpress.com/Random-Circulant-Matrices/Bose-Saha/p/book/9781138351097
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Slot 1368 (0 Floor, East Wing) Non-fiction 512.9434 B6R2 (Browse shelf) Not for Issue 199232

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

Appendix

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.

https://www.crcpress.com/Random-Circulant-Matrices/Bose-Saha/p/book/9781138351097

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