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عنوان
Patterned Random Matrices /

پدید آورنده
Arup Bose.

موضوع
Algebras, Linear.,Multilinear algebra.,Probabilities.,Random matrices.,Random variables.,Statistics.,Algebras, Linear.,MATHEMATICS-- Applied.,MATHEMATICS-- Probability & Statistics-- General.,Multilinear algebra.,Probabilities.,Random matrices.,Random variables.,Statistics.

رده
QA273

کتابخانه
Center and Library of Islamic Studies in European Languages

محل استقرار
استان: Qom ـ شهر: Qom

Center and Library of Islamic Studies in European Languages

تماس با کتابخانه : 32910706-025

INTERNATIONAL STANDARD BOOK NUMBER

(Number (ISBN
0429488432
(Number (ISBN
0429948883
(Number (ISBN
0429948891
(Number (ISBN
9780429488436
(Number (ISBN
9780429948886
(Number (ISBN
9780429948893
Erroneous ISBN
1138591467
Erroneous ISBN
9781138591462

TITLE AND STATEMENT OF RESPONSIBILITY

Title Proper
Patterned Random Matrices /
General Material Designation
[Book]
First Statement of Responsibility
Arup Bose.

EDITION STATEMENT

Edition Statement
First edition.

.PUBLICATION, DISTRIBUTION, ETC

Place of Publication, Distribution, etc.
Boca Raton, FL :
Name of Publisher, Distributor, etc.
CRC Press,
Date of Publication, Distribution, etc.
2018.

PHYSICAL DESCRIPTION

Specific Material Designation and Extent of Item
1 online resource :
Other Physical Details
text file, PDF

INTERNAL BIBLIOGRAPHIES/INDEXES NOTE

Text of Note
Includes bibliographical references and index.

CONTENTS NOTE

Text of Note
2.2 Toeplitz and Hankel matrices2.2.1 Toeplitz matrix; 2.2.2 Hankel matrix; 2.3 Reverse Circulant matrix; 2.4 Symmetric Circulant and related matrices; 2.5 Additional properties of the LSDs; 2.5.1 Moments of the Toeplitz and Hankel LSDs; 2.5.2 Contribution of words and comparison of LSDs; 2.5.3 Unbounded support of the Toeplitz and Hankel LSDs; 2.5.4 Non-unimodality of the Hankel LSD; 2.5.5 Density of the Toeplitz LSD; 2.5.6 Pyramidal multiplicativity; 2.6 Exercises; Chapter 3 Patterned XX' matrices; 3.1 A unified setup; 3.2 Aspect ratio y = 0; 3.2.1 Preliminaries.
Text of Note
3.2.2 Sample variance-covariance matrix3.2.2.1 Catalan words and the Marˇcenko-Pastur law; 3.2.2.2 LSD; 3.2.3 Other XX0 matrices; 3.3 Aspect ratio y = 0; 3.3.1 Sample variance-covariance matrix; 3.3.2 Other XX0 matrices; 3.4 Exercises; Chapter 4 k-Circulant matrices; 4.1 Normal approximation; 4.2 Circulant matrix; 4.3 k-Circulant matrices; 4.3.1 Eigenvalues; 4.3.2 Eigenvalue partition; 4.3.3 Lower-order elements; 4.3.4 Degenerate limit; 4.3.5 Non-degenerate limit; 4.4 Exercises; Chapter 5 Wigner-type matrices; 5.1 Wigner-type matrix; 5.2 Exercises
Text of Note
9.3 Nature of the limit9.4 Exercises; Chapter 10 Joint convergence of independent patternedmatrices; 10.1 Definitions and notation; 10.2 Joint convergence; 10.3 Freeness; 10.4 Sum of independent patterned matrices; 10.5 Proofs; 10.6 Exercises; Chapter 11 Autocovariance matrix; 11.1 Preliminaries; 11.2 Main results; 11.3 Proofs; 11.4 Exercises; Bibliography; Index.
Text of Note
Chapter 6 Balanced Toeplitz and Hankel matrices6.1 Main results; 6.2 Exercises; Chapter 7 Patterned band matrices; 7.1 LSD for band matrices; 7.2 Proof; 7.2.1 Reduction to uniformly bounded input; 7.2.2 Trace formula, circuits, words and matches; 7.2.3 Negligibility of higher-order edges; 7.2.4 (M1) condition; 7.3 Exercises; Chapter 8 Triangular matrices; 8.1 General pattern; 8.2 Triangular Wigner matrix; 8.2.1 LSD; 8.2.2 Contribution of Catalan words; 8.3 Exercises; Chapter 9 Joint convergence of i.i.d. patterned matrices; 9.1 Non-commutative probability space; 9.2 Joint convergence.
Text of Note
Cover; Half Title; Title; Copyright; Contents; Preface; Introduction; About the Author; Chapter 1 A unified framework; 1.1 Empirical and limiting spectral distribution; 1.2 Moment method; 1.3 A metric for probability measures; 1.4 Patterned matrices: A unified approach; 1.4.1 Scaling; 1.4.2 Reduction to bounded case; 1.4.3 Trace formula and circuits; 1.4.4 Words; 1.4.5 Vertices; 1.4.6 Pair-matched word; 1.4.7 Sub-sequential limit; 1.5 Exercises; Chapter 2 Common symmetric patterned matrices; 2.1 Wigner matrix; 2.1.1 Semi-circle law, non-crossing partitions, Catalan words; 2.1.2 LSD.
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SUMMARY OR ABSTRACT

Text of Note
"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. 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 Sankyh? 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."--Provided by publisher.

ACQUISITION INFORMATION NOTE

Source for Acquisition/Subscription Address
Ingram Content Group
Stock Number
9780429948886

OTHER EDITION IN ANOTHER MEDIUM

International Standard Book Number
9780429948886

TOPICAL NAME USED AS SUBJECT

Algebras, Linear.
Multilinear algebra.
Probabilities.
Random matrices.
Random variables.
Statistics.
Algebras, Linear.
MATHEMATICS-- Applied.
MATHEMATICS-- Probability & Statistics-- General.
Multilinear algebra.
Probabilities.
Random matrices.
Random variables.
Statistics.

(SUBJECT CATEGORY (Provisional

MAT-- 003000
MAT-- 029000
MAT002000
MAT029010

DEWEY DECIMAL CLASSIFICATION

Number
519
.
2
Number
SCMA60
Number
WB020
Number
WB021
Number
WB057
Number
WB075
Edition
23

LIBRARY OF CONGRESS CLASSIFICATION

Class number
QA273

PERSONAL NAME - PRIMARY RESPONSIBILITY

Bose, Arup

ORIGINATING SOURCE

Date of Transaction
20200822163230.0
Cataloguing Rules (Descriptive Conventions))
pn

ELECTRONIC LOCATION AND ACCESS

Electronic name
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