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Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications /

The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite mome...

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Bibliographic Details
Main Authors: Bai, Zhidong (Author)
Corporate Authors: World Scientific (Firm)
Group Author: Fang, Zhaoben; Liang, Ying-Chang
Published: World Scientific Pub. Co.,
Publisher Address: Singapore ; Hackensack, N.J. :
Publication Dates: 2014.
Literature type: eBook
Language: English
Subjects:
Random matrices.
Electronic books.
Online Access: http://www.worldscientific.com/worldscibooks/10.1142/9049#t=toc
Summary: The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.
Carrier Form: 1 online resource (xi,220pages) : illustrations
Bibliography: Includes bibliographical references (pages 201-215) and index.
ISBN: 9789814579063
Index Number: QA188
CLC: O151.21
Contents: 1. Introduction. 1.1. History of RMT and current development. 1.2. Applications to wireless communications. 1.3. Applications to finance statistics -- 2. Limiting spectral distributions. 2.1. Semicircular law. 2.2. Marcenko-Pastur law. 2.3. LSD of products. 2.4. Hadamard product. 2.5. Circular law -- 3. Extreme eigenvalues. 3.1. Wigner matrix. 3.2. Sample covariance matrix. 3.3. Spectrum separation. 3.4. Tracy-Widom law -- 4. Central limit theorems of linear spectral statistics. 4.1. Motivation and strategy. 4.2. CLT of LSS for Wigner matrix. 4.3. CLT of LSS for sample covariance matrices. 4.4. F matrix -- 5. Limiting behavior of eigenmatrix of sample covariance matrix. 5.1 Earlier work by Silverstein. 5.2. Further extension of Silverstein's work. 5.3. Projecting the eigenmatrix to a d-dimensional space -- 6. Wireless communications. 6.1. Introduction. 6.2. Channel models. 6.3. Channel capacity for MIMO antenna systems. 6.4. Limiting capacity of random MIMO channels. 6.5. Concluding remarks -- 7. Limiting performances of linear and iterative receivers. 7.1. Introduction. 7.2. Linear equalizers. 7.3. Limiting SINR analysis for linear receivers. 7.4. Iterative receivers. 7.5. Limiting performance of iterative receivers. 7.6. Numerical results. 7.7. Concluding remarks -- 8. Application to finance. 8.1. Portfolio and risk management. 8.2. Factor models .. 8.3. Some application in finance of factor model.

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