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Random matrix theory and its applications [[electronic resource] ] : multivariate statistics and wireless communications / / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang
| Random matrix theory and its applications [[electronic resource] ] : multivariate statistics and wireless communications / / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (176 p.) |
| Disciplina | 512.9434 |
| Altri autori (Persone) |
BaiZhidong
ChenYang (Mathematics teacher) LiangYing-Chang |
| Collana | Lecture notes series, Institute for Mathematical Sciences, National University of Singapore |
| Soggetto topico | Random matrices |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-75804-7
9786612758041 981-4273-12-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910455882803321 |
| Hackensack, N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random matrix theory and its applications [[electronic resource] ] : multivariate statistics and wireless communications / / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang
| Random matrix theory and its applications [[electronic resource] ] : multivariate statistics and wireless communications / / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (176 p.) |
| Disciplina | 512.9434 |
| Altri autori (Persone) |
BaiZhidong
ChenYang (Mathematics teacher) LiangYing-Chang |
| Collana | Lecture notes series, Institute for Mathematical Sciences, National University of Singapore |
| Soggetto topico | Random matrices |
| ISBN |
1-282-75804-7
9786612758041 981-4273-12-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910780727203321 |
| Hackensack, N.J., : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||