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Patterned Random Matrices

Patterned Random Matrices

This book focuses on the limit spectral distribution (LSD) of patterned random matrices and provides a comprehensive variety of LSD results. It is accessible to first or second years Master's students and uses very elementary techniques. It is suitable for a beginner in random ma... read full description below.

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ISBN 9781138591462
Barcode 9781138591462
Published 17 May 2018 by Taylor & Francis Ltd
Format Hardback
Author(s) By Bose, Arup
Availability In stock at publisher; ships 6-12 working days

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Full details for this title

ISBN-13 9781138591462
ISBN-10 1138591467
Stock Available
Status In stock at publisher; ships 6-12 working days
Publisher Taylor & Francis Ltd
Imprint CRC Press
Publication Date 17 May 2018
International Publication Date 2 July 2018
Publication Country United Kingdom United Kingdom
Format Hardback
Author(s) By Bose, Arup
Category Algebra
Probability & Statistics
Number of Pages 269
Dimensions Width: 156mm
Height: 235mm
Weight 567g
Interest Age 19+ years
Reading Age 19+ years
Library of Congress Random matrices
NBS Text Science & Mathematics: Textbooks & Study Guides
ONIX Text College/higher education
Dewey Code 512.9434
Catalogue Code Not specified

Description of this Book

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 method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the MarchA enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. 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 Sankyha 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.

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Awards, Reviews & Star Ratings

NZ Review . . . 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

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Author's Bio

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 Sankyha 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.

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