Random matrix theory and its applications : multivariate statistics and wireless communications

Random matrix theory and its applications : multivariate statistics and wireless communications / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang.

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...

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Bibliographic Details
Other Authors: Bai, Zhidong, Chen, Yang, Liang, Ying-Chang
Format: eBook
Language:English
Published: Hackensack, NJ : World Scientific, ©2009.
Series:Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; v. 18.
Subjects:
Random matrices.
MATHEMATICS > Algebra > Intermediate.
Random matrices
Online Access:Click for online access
Table of Contents:
  • 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.
  • 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.
  • 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.
  • 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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