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" Random matrix theory and its applications : "
editors, Zhidong Bai, Yang Chen, Ying-Chang Liang.
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BL
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| Record Number
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953057
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b707427
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| Title & Author
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Random matrix theory and its applications : : multivariate statistics and wireless communications /\ editors, Zhidong Bai, Yang Chen, Ying-Chang Liang.
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| Publication Statement
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Hackensack, NJ :: World Scientific,, ©2009.
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| Series Statement
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Lecture notes series,; v. 18
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| Page. NO
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1 online resource (x, 165 pages) :: illustrations
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| ISBN
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1282758047
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: 661275804X
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: 9781282758049
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: 9786612758041
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: 9789814273121
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: 9814273120
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9789814273114
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9814273112
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Foreword; Preface; The Stieltjes Transform and its Role in Eigenvalue Behavior of Large Dimensional Random Matrices Jack W. Silverstein; 1. Introduction; 2. Why These Theorems are True; 3. The Other Equations; 4. Proof of Uniqueness of (1.1); 5. Truncation and Centralization; 6. The Limiting Distributions; 7. Other Uses of the Stieltjes Transform; References; Beta Random Matrix Ensembles Peter J. Forrester; 1. Introduction; 1.1. Log-gas systems; 1.2. Quantum many body systems; 1.3. Selberg correlation integrals; 1.4. Correlation functions; 1.5. Scaled limits.
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2. Physical Random Matrix Ensembles2.1. Heavy nuclei and quantum mechanics; 2.2. Dirac operators and QCD; 2.3. Random scattering matrices; 2.4. Quantum conductance problems; 2.5. Eigenvalue p.d.f.'s for Hermitian matrices; 2.6. Eigenvalue p.d.f.'s for Wishart matrices; 2.7. Eigenvalue p.d.f.'s for unitary matrices; 2.8. Eigenvalue p.d.f.'s for blocks of unitary matrices; 2.9. Classical random matrix ensembles; 3.-Ensembles of Random Matrices; 3.1. Gaussian ensemble; 4. Laguerre Ensemble; 5. Recent Developments; Acknowledgments; References.
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8. Example: Analysis of Large CDMA Systems8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References.
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Future of Statistics Zhidong Bai and Shurong Zheng1. Introduction; 2. A Multivariate Two-Sample Problem; 2.1. Asymptotic power of T 2 test; 2.2. Dempster's NET; 2.3. Bai and Saranadasa's ANT; 2.4. Conclusions and simulations; 3. A Likelihood Ratio Test on Covariance Matrix; 3.1. Classical tests; 3.2. Random matrix theory; 3.3. Testing based on RMT limiting CLT; 3.4. Simulation results; 4. Conclusions; Acknowledgment; References; The and Shannon Transforms: A Bridge between Random Matrices and Wireless Communications Antonia M. Tulino; 1. Introduction; 2. Wireless Communication Channels.
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| Abstract
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Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists. In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, th.
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| Subject
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Random matrices.
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Algebra.
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Mathematics.
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Physical Sciences Mathematics.
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Random matrices.
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MATHEMATICS-- Algebra-- Intermediate.
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Random matrices.
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| Dewey Classification
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512
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| LC Classification
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QA188.R36 2009eb
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| Added Entry
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Bai, Zhidong.
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Chen, Yang.
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Liang, Ying-Chang.
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