《高維隨機矩陣的譜理論及其在無線通信和金融統計中的套用》是2009年中國科學技術大學出版社出版的圖書，作者是白志東，方兆本，梁應敞。
基本介紹
- 書名：高維隨機矩陣的譜理論及其在無線通信和金融統計中的套用
- 作者：白志東，方兆本，梁應敞
- ISBN：9787312022746
- 出版社：中國科學技術大學出版社
- 出版時間： 2009-6-1
- 開本：16開
內容簡介,圖書目錄,
內容簡介
本書由中國科學技術大學出版社出版，講解了隨機矩陣譜理論的主要結果和前瞻研究，以及它在無線通信和現代金融風險理論中的套用。書中前面講解基本知識，後面分析重要範例，全面介紹了隨機矩陣譜理論在這兩個領域中的成果。本書對其他需要高維數據分析的領域，能起到示範作用。本書可作為統計學、計算機科學、現代物理、量子力學、無線通信、金融工程、經濟學等領域本科生、研究生和工程技術人員學習隨機矩陣理論的重要參考資料。
圖書目錄
Preface of Alumni's Serials
Preface
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 Central Limit Theory (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 Semi-circular Law
2.1.1 The lid Case
2.1.2 Independent but not Identically Distributed
2.2 Marcenko-Pastur Law
2.2.1 MP Law for lid Case
2.2.2 Generalization to the Non-lid 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 4
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 Matrices
2.5.2 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 CLT of LSS
4.1 Motivation and Strategy
4.2 CLT of LSS for Wigner Matrix
4.2.1 Outlines of the Proof
4.3 CLT of LSS for Sample Covariance Matrices
4.4 F Matrix
4.4.1 Decomposition of Xnf
4.4.2 Limiting Distribution of X+nf
4.4.3 Limiting Distribution of Xnf
5 Limiting Behavior of Eigenmatrix of Sample Covariance Matrix
5.1 Earlier Work by Silverstein
5.2 Further Extension of Silverstein's Work
5.3 Projecting the Eigenmatrix to a d-Dimensional Space
5.3.1 Main Results
5.3.2 Sketch of Proof of Theorem 5.19
5.3.3 Proof of Corollary 5.23
6 Applications to Wireless Communications
6.1 Introduction
6.2 Channel Models.
6.2.1 Basics of Wireless Communication Systems
……
7 Limiting Performances of Linear and Iterative Receivers
8 Applications to Finace Statistics
References
Index
