Random circulant matrices/ Arup Bose, Koushik Saha
Material type:
TextPublication details: Boca Raton: CRC Press, 2019Description: xix, 192 pages 23.5 cmISBN: - 9781138351097
- 512.9434 23 B743
| 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 |
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| 512.9434 B666 Matrix calculus | 512.9434 B732 Matrix-tensor methods in continuum mechanics | 512.9434 B732 Matrix-tensor methods in continuum mechanics | 512.9434 B743 Random circulant matrices/ | 512.9434 B751 Introduction to large truncated Toeplitz matrices | 512.9434 B751 Spectral properties of banded Toeplitz matrices | 512.9434 B758 Products of random matrices with applications to Schrodinger operations |
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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