Author(s): Zhi Dong Bai, Zhi Dong Bai, Yang Chen, Ying-chang Liang
Series: Lecture Notes Series, Institute for Mathematical Sciences, ... Sciences, National University of Singapore
Publisher: WS
Year: 2009
Language: English
Pages: 174
Cover......Page 1
Half Title......Page 2
LECTURE NOTES SERIES......Page 3
Title......Page 4
Copyright......Page 5
CONTENTS......Page 6
Foreword ......Page 8
Preface ......Page 10
1. Introduction......Page 12
2. Why These Theorems are True......Page 16
3. The Other Equations......Page 20
4. Proof of Uniqueness of (1.1)......Page 23
5. Truncation and Centralization......Page 24
6. The Limiting Distributions......Page 27
7. Other Uses of the Stieltjes Transform......Page 31
References......Page 36
1.1. Log-gas systems......Page 37
1.2. Quantum many body systems......Page 40
1.3. Selberg correlation integrals......Page 42
1.4. Correlation functions......Page 45
1.5. Scaled limits......Page 50
2.1. Heavy nuclei and quantum mechanics......Page 53
2.3. Random scattering matrices......Page 55
2.4. Quantum conductance problems......Page 56
2.5. Eigenvalue p.d.f.'s for Hermitian matrices......Page 57
2.6. Eigenvalue p.d.f.'s for Wishart matrices......Page 60
2.7. Eigenvalue p.d.f.'s for unitary matrices......Page 61
2.8. Eigenvalue p.d.f.'s for blocks of unitary matrices......Page 63
3.1. Gaussian B ensemble......Page 65
3.2. Three term recurrence and tridiagonal matrices......Page 71
4. Laguerre B Ensemble......Page 72
5. Recent Developments......Page 75
References......Page 76
1. Introduction......Page 79
2. A Multivariate Two-Sample Problem......Page 80
2.1. Asymptotic power of T² test......Page 81
2.2. Dempster's NET......Page 83
2.3. Bai and Saranadasa's ANT......Page 85
2.4. Conclusions and simulations......Page 87
3.1. Classical tests......Page 89
3.2. Random matrix theory......Page 92
3.3. Testing based on RMT limiting CLT......Page 95
3.4. Simulation results......Page 97
References......Page 102
1. Introduction......Page 104
2. Wireless Communication Channels......Page 105
3. Why Asymptotic Random Matrix Theory?......Page 106
4. η and Shannon Transforms: Theory and Applications......Page 112
5. Applications to Wireless Communications......Page 122
5.1.1. DS-CDMA frequency-flat fading......Page 123
5.1.2. Multi-carrier CDMA......Page 127
5.2. Multi-antenna channels......Page 130
5.3. Separable correlation model......Page 131
5.4. Non-separable correlation model......Page 136
5.5. Non-ergodic channels......Page 140
References......Page 142
1. Introduction......Page 148
2. Self Average......Page 149
3. Free Energy......Page 150
4. The Meaning of the Energy Function......Page 151
5. Replica Continuity......Page 153
6. Saddle Point Integration......Page 154
7. Replica Symmetry......Page 155
8. Example: Analysis of Large CDMA Systems......Page 156
8.1. Gaussian prior distribution......Page 162
8.2. Binary prior distribution......Page 165
8.3. Arbitrary prior distribution......Page 169
9. Phase Transitions......Page 171
References......Page 173
