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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 | ||
| ||