1st Edition

Patterned Random Matrices

By Arup Bose Copyright 2018
291 Pages
by Chapman & Hall

292 Pages
by Chapman & Hall

291 Pages
by Chapman & Hall

Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the... Read more

1. A unified framework

2. Common symmetric patterned matrices

3. Patterned XX matrices

4. 
k-Circulant matrices

5. Wigner type matrices

6. Balanced Toeplitz and Hankel matrices

7. Triangular matrices

8. Joint convergence of iid patterned matrices

9. Joint convergence of independent patterned matrices

10. Autocovariance matrix



Biography

Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

". . . this book can be recommended for students and researchers interested in a broad overview of random matrix theory. Each chapter ends with plenty of problems useful for exercises and training." ~ Statistical Papers

" . . . the authors should be congratulated for producing two highly relevant and well-written books. Statisticians would probably gravitate to LCAM in the first instance and those working in linear algebra would probably gravitate to PRM." ~Jonathan Gillard, Cardiff University