Patterned random matrices (Record no. 211935)

000 -LEADER
fixed length control field aam a22 4500
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 190507b 2018 ||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781138591462
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.9434
Item number B6P2
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Bose, Arup
9 (RLIN) 379089
245 ## - TITLE STATEMENT
Title Patterned random matrices
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher, distributor, etc CRC Press
Date of publication, distribution, etc 2018
Place of publication, distribution, etc Florida
300 ## - PHYSICAL DESCRIPTION
Extent xxi, 267p.
Other physical details With index
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Table of Contents

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 Patterned band matrices
8 Triangular matrices
9 Joint convergence of i.i.d. patterned matrices
10 Joint convergence of independent patterned matrices
11 Autocovariance matrix
520 ## - SUMMARY, ETC.
Summary, etc 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 March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.

https://www.crcpress.com/Patterned-Random-Matrices/Bose/p/book/9781138591462
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Probabilities
9 (RLIN) 379602
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Random matrices
9 (RLIN) 379603
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Random variables
9 (RLIN) 379604
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Linear - Multilinear algebra
9 (RLIN) 379605
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Probability theory - Applications
9 (RLIN) 379606
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Permanent location Current location Shelving location Date acquired Source of acquisition Cost, normal purchase price Item location Full call number Barcode Date last seen Cost, replacement price Koha item type
        Not for Issue Non-fiction Vikram Sarabhai Library Vikram Sarabhai Library General Stacks 2019-05-06 2 7.00 Slot 1368 (0 Floor, East Wing) 512.9434 B6P2 199347 2019-05-06 9560.00 Books

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