01574aam a2200181 4500008004500000020001800045082001900063100001500082245003000097260002900127300002700156504032500183520078300508650003601291650002001327650001601347700002901363190426b 2019 ||||| |||| 00| 0 eng d a9781138351097 a512.9434bB6R2 aBose, Arup aRandom circulant matrices bCRC Pressc2019aFlorida axix, 192p.bWith index aTable 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 aCirculant 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 aMatrices -- Problems, exercises aRandom matrices aEigenvalues aSaha, KoushikeCo author