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

• Record Nr.: UNINA9910455882803321
• Pubbl/distr/stampa: Hackensack, N.J., : World Scientific, c2009
• ISBN: 1-282-75804-7; 9786612758041; 981-4273-12-0
• Descrizione fisica: 1 online resource (176 p.)
• Collana: Lecture notes series, Institute for Mathematical Sciences, National University of Singapore, , 1793-0758 ; ; v. 18
• Altri autori (Persone): BaiZhidong; ChenYang (Mathematics teacher); LiangYing-Chang
• Disciplina: 512.9434
• Soggetti: Random matrices; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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 Ensembles 2.1. 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 Zheng 1. 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; 3. Why Asymptotic Random Matrix Theory? 4. η and Shannon Transforms: Theory and Applications; 5. Applications to Wireless Communications; 5.1. CDMA; 5.1.1. DS-CDMA frequency-flat fading; 5.1.2. Multi-carrier CDMA; 5.2. Multi-antenna channels; 5.3. Separable correlation model; 5.4. Non-separable correlation model; 5.5. Non-ergodic channels; References; The Replica Method in Multiuser Communications Ralf R. Muller; 1. Introduction; 2. Self Average; 3. Free Energy; 4. The Meaning of the Energy Function; 5. Replica Continuity; 6. Saddle Point Integration; 7. Replica Symmetry; 8. Example: Analysis of Large CDMA Systems 8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References
• Sommario/riassunto: 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 1990's, 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,