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Random circulant matrices/ Arup Bose, Koushik Saha

By: Contributor(s): Material type: TextTextPublication details: Boca Raton: CRC Press, 2019Description: xix, 192 pages 23.5 cmISBN:
  • 9781138351097
Subject(s): DDC classification:
  • 512.9434 23 B743
Contents:
1. Circulants -- 2. Symmetric and reverse circulant -- 3.LSD: normal approximation -- 4. LSD: dependent input -- 5. Spectral radius: light tail -- 6. Spectral radius: k-circulant -- 7. Maximum of scaled eigenvalues: dependent input -- 8. Poisson convergence -- 9. Heavy tailed input: LSD -- 10. Heavy-tailed input: spectral radius -- 11. Appendix
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.9434 B743 (Browse shelf(Opens below)) Available 138468
Total holds: 0

Includes Bibliographical References and Index

1. Circulants -- 2. Symmetric and reverse circulant -- 3.LSD: normal approximation -- 4. LSD: dependent input -- 5. Spectral radius: light tail -- 6. Spectral radius: k-circulant -- 7. Maximum of scaled eigenvalues: dependent input -- 8. Poisson convergence -- 9. Heavy tailed input: LSD -- 10. Heavy-tailed input: spectral radius -- 11. 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.

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