Random circulant matrices
Bose, Arup
creator
Saha, Koushik
Co author
text
Florida
CRC Press
2019
monographic
| 0
xix, 192p. With index
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
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
Matrices -- Problems, exercises
Random matrices
Eigenvalues
512.9434 B6R2
9781138351097
190426