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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 | ||
| ||
Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, the Singapore Infocomm Research Institute, Singapore
| Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, the Singapore Infocomm Research Institute, Singapore |
| Autore | Bai Zhidong |
| Pubbl/distr/stampa | Singapore : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (233 p.) |
| Disciplina | 519.2 |
| Soggetto topico | Random matrices |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4579-06-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1 Introduction; 1.1 History of RMT and Current Development; 1.1.1 A brief review of RMT; 1.1.2 Spectral Analysis of Large Dimensional Random Matrices; 1.1.3 Limits of Extreme Eigenvalues; 1.1.4 Convergence Rate of ESD; 1.1.5 Circular Law; 1.1.6 CLT of Linear Spectral Statistics; 1.1.7 Limiting Distributions of Extreme Eigenvalues and Spacings; 1.2 Applications to Wireless Communications; 1.3 Applications to Finance Statistics; 2 Limiting Spectral Distributions; 2.1 Semicircular Law; 2.1.1 The iid Case; 2.1.2 Independent but not Identically Distributed
2.2 Marcenko-Pastur Law2.2.1 MP Law for iid Case; 2.2.2 Generalization to the Non-iid Case; 2.2.3 Proof of Theorem 2.11 by Stieltjes Transform; 2.3 LSD of Products; 2.3.1 Existence of the ESD of SnTn; 2.3.2 Truncation of the ESD of Tn; 2.3.3 Truncation, Centralization and Rescaling of the X-variables; 2.3.4 Sketch of the Proof of Theorem 2.12; 2.3.5 LSD of F Matrix; 2.3.6 Sketch of the Proof of Theorem 2.14; 2.3.7 When T is a Wigner Matrix; 2.4 Hadamard Product; 2.4.1 Truncation and Centralization; 2.4.2 Outlines of Proof of the theorem; 2.5 Circular Law 2.5.1 Failure of Techniques Dealing with Hermitian Matrices2.5.2 Revisit of Stieltjes Transformation; 2.5.3 A Partial Answer to the Circular Law; 2.5.4 Comments and Extensions of Theorem 2.33; 3 Extreme Eigenvalues; 3.1 Wigner Matrix; 3.2 Sample Covariance Matrix; 3.2.1 Spectral Radius; 3.3 Spectrum Separation; 3.4 Tracy-Widom Law; 3.4.1 TW Law for Wigner Matrix; 3.4.2 TW Law for Sample Covariance Matrix; 4 Central Limit Theorems of Linear Spectral Statistics; 4.1 Motivation and Strategy; 4.2 CLT of LSS for Wigner Matrix; 4.2.1 Outlines of the Proof 6.2.3 Random Matrix Channels6.2.4 Linearly Precoded Systems; 6.3 Channel Capacity for MIMO Antenna Systems; 6.3.1 Single-Input Single-Output Channels; 6.3.2 MIMO Fading Channels; 6.4 Limiting Capacity of Random MIMO Channels; 6.4.1 CSI-Unknown Case; 6.4.2 CSI-Known Case; 6.5 Concluding Remarks; 7 Limiting Performances of Linear and Iterative Receivers; 7.1 Introduction; 7.2 Linear Equalizers; 7.2.1 ZF Equalizer; 7.2.2 Matched Filter (MF) Equalizer; 7.2.3 MMSE Equalizer; 7.2.4 Suboptimal MMSE Equalizer; 7.3 Limiting SINR Analysis for Linear Receivers; 7.3.1 Random Matrix Channels 7.3.2 Linearly Precoded Systems |
| Record Nr. | UNINA-9910464693803321 |
Bai Zhidong
|
||
| Singapore : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, The Singapore Infocomm Research Institute, Singapore
| Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, The Singapore Infocomm Research Institute, Singapore |
| Autore | Bai Zhidong |
| Pubbl/distr/stampa | Singapore : , : World Scientific : , : University of Science and Technology of China Press, , [2014] |
| Descrizione fisica | 1 online resource (xi, 220 pages) : illustrations (some color) |
| Disciplina | 519.2 |
| Collana | Gale eBooks |
| Soggetto topico |
Random matrices
Spectral theory (Mathematics) Wireless communication systems Finance - Statistics |
| ISBN | 981-4579-06-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1 Introduction; 1.1 History of RMT and Current Development; 1.1.1 A brief review of RMT; 1.1.2 Spectral Analysis of Large Dimensional Random Matrices; 1.1.3 Limits of Extreme Eigenvalues; 1.1.4 Convergence Rate of ESD; 1.1.5 Circular Law; 1.1.6 CLT of Linear Spectral Statistics; 1.1.7 Limiting Distributions of Extreme Eigenvalues and Spacings; 1.2 Applications to Wireless Communications; 1.3 Applications to Finance Statistics; 2 Limiting Spectral Distributions; 2.1 Semicircular Law; 2.1.1 The iid Case; 2.1.2 Independent but not Identically Distributed
2.2 Marcenko-Pastur Law2.2.1 MP Law for iid Case; 2.2.2 Generalization to the Non-iid Case; 2.2.3 Proof of Theorem 2.11 by Stieltjes Transform; 2.3 LSD of Products; 2.3.1 Existence of the ESD of SnTn; 2.3.2 Truncation of the ESD of Tn; 2.3.3 Truncation, Centralization and Rescaling of the X-variables; 2.3.4 Sketch of the Proof of Theorem 2.12; 2.3.5 LSD of F Matrix; 2.3.6 Sketch of the Proof of Theorem 2.14; 2.3.7 When T is a Wigner Matrix; 2.4 Hadamard Product; 2.4.1 Truncation and Centralization; 2.4.2 Outlines of Proof of the theorem; 2.5 Circular Law 2.5.1 Failure of Techniques Dealing with Hermitian Matrices2.5.2 Revisit of Stieltjes Transformation; 2.5.3 A Partial Answer to the Circular Law; 2.5.4 Comments and Extensions of Theorem 2.33; 3 Extreme Eigenvalues; 3.1 Wigner Matrix; 3.2 Sample Covariance Matrix; 3.2.1 Spectral Radius; 3.3 Spectrum Separation; 3.4 Tracy-Widom Law; 3.4.1 TW Law for Wigner Matrix; 3.4.2 TW Law for Sample Covariance Matrix; 4 Central Limit Theorems of Linear Spectral Statistics; 4.1 Motivation and Strategy; 4.2 CLT of LSS for Wigner Matrix; 4.2.1 Outlines of the Proof 6.2.3 Random Matrix Channels6.2.4 Linearly Precoded Systems; 6.3 Channel Capacity for MIMO Antenna Systems; 6.3.1 Single-Input Single-Output Channels; 6.3.2 MIMO Fading Channels; 6.4 Limiting Capacity of Random MIMO Channels; 6.4.1 CSI-Unknown Case; 6.4.2 CSI-Known Case; 6.5 Concluding Remarks; 7 Limiting Performances of Linear and Iterative Receivers; 7.1 Introduction; 7.2 Linear Equalizers; 7.2.1 ZF Equalizer; 7.2.2 Matched Filter (MF) Equalizer; 7.2.3 MMSE Equalizer; 7.2.4 Suboptimal MMSE Equalizer; 7.3 Limiting SINR Analysis for Linear Receivers; 7.3.1 Random Matrix Channels 7.3.2 Linearly Precoded Systems |
| Record Nr. | UNINA-9910789294903321 |
|
Bai Zhidong
|
||
| Singapore : , : World Scientific : , : University of Science and Technology of China Press, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, The Singapore Infocomm Research Institute, Singapore
| Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics : random matrix theory and its applications / / Zhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, The Singapore Infocomm Research Institute, Singapore |
| Autore | Bai Zhidong |
| Pubbl/distr/stampa | Singapore : , : World Scientific : , : University of Science and Technology of China Press, , [2014] |
| Descrizione fisica | 1 online resource (xi, 220 pages) : illustrations (some color) |
| Disciplina | 519.2 |
| Collana | Gale eBooks |
| Soggetto topico |
Random matrices
Spectral theory (Mathematics) Wireless communication systems Finance - Statistics |
| ISBN | 981-4579-06-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1 Introduction; 1.1 History of RMT and Current Development; 1.1.1 A brief review of RMT; 1.1.2 Spectral Analysis of Large Dimensional Random Matrices; 1.1.3 Limits of Extreme Eigenvalues; 1.1.4 Convergence Rate of ESD; 1.1.5 Circular Law; 1.1.6 CLT of Linear Spectral Statistics; 1.1.7 Limiting Distributions of Extreme Eigenvalues and Spacings; 1.2 Applications to Wireless Communications; 1.3 Applications to Finance Statistics; 2 Limiting Spectral Distributions; 2.1 Semicircular Law; 2.1.1 The iid Case; 2.1.2 Independent but not Identically Distributed
2.2 Marcenko-Pastur Law2.2.1 MP Law for iid Case; 2.2.2 Generalization to the Non-iid Case; 2.2.3 Proof of Theorem 2.11 by Stieltjes Transform; 2.3 LSD of Products; 2.3.1 Existence of the ESD of SnTn; 2.3.2 Truncation of the ESD of Tn; 2.3.3 Truncation, Centralization and Rescaling of the X-variables; 2.3.4 Sketch of the Proof of Theorem 2.12; 2.3.5 LSD of F Matrix; 2.3.6 Sketch of the Proof of Theorem 2.14; 2.3.7 When T is a Wigner Matrix; 2.4 Hadamard Product; 2.4.1 Truncation and Centralization; 2.4.2 Outlines of Proof of the theorem; 2.5 Circular Law 2.5.1 Failure of Techniques Dealing with Hermitian Matrices2.5.2 Revisit of Stieltjes Transformation; 2.5.3 A Partial Answer to the Circular Law; 2.5.4 Comments and Extensions of Theorem 2.33; 3 Extreme Eigenvalues; 3.1 Wigner Matrix; 3.2 Sample Covariance Matrix; 3.2.1 Spectral Radius; 3.3 Spectrum Separation; 3.4 Tracy-Widom Law; 3.4.1 TW Law for Wigner Matrix; 3.4.2 TW Law for Sample Covariance Matrix; 4 Central Limit Theorems of Linear Spectral Statistics; 4.1 Motivation and Strategy; 4.2 CLT of LSS for Wigner Matrix; 4.2.1 Outlines of the Proof 6.2.3 Random Matrix Channels6.2.4 Linearly Precoded Systems; 6.3 Channel Capacity for MIMO Antenna Systems; 6.3.1 Single-Input Single-Output Channels; 6.3.2 MIMO Fading Channels; 6.4 Limiting Capacity of Random MIMO Channels; 6.4.1 CSI-Unknown Case; 6.4.2 CSI-Known Case; 6.5 Concluding Remarks; 7 Limiting Performances of Linear and Iterative Receivers; 7.1 Introduction; 7.2 Linear Equalizers; 7.2.1 ZF Equalizer; 7.2.2 Matched Filter (MF) Equalizer; 7.2.3 MMSE Equalizer; 7.2.4 Suboptimal MMSE Equalizer; 7.3 Limiting SINR Analysis for Linear Receivers; 7.3.1 Random Matrix Channels 7.3.2 Linearly Precoded Systems |
| Record Nr. | UNINA-9910807350903321 |
|
Bai Zhidong
|
||
| Singapore : , : World Scientific : , : University of Science and Technology of China Press, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||