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内容简介

本书讲述了随机矩阵谱理论的主要结果和前瞻研究，以及它在无线通信和现代金融风险理论中的应用。书中前面讲解基本知识，后面分析重要范例，全面介绍了随机矩阵谱理论在这两个领域中的成果。本书对其他需要高维数据分析的领域，能起到示范作用。本书可作为统计学、计算机科学、现代物理、量子力学、无线通信、金融工程、经济学等领域本科生、研究生和工程技术人员学习随机矩阵理论的重要参考资料。

目录

Preface of Alumnis 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 Silversteins 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

前言/序言

高维随机矩阵的谱理论及其在无线通信和金融统计中的应用（全英文） 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

书很薄，价格很贵，内容不简单……

评分☆☆☆☆☆

喜欢这书很久了，这次正好碰到京东有，立马拿下。

评分☆☆☆☆☆

要是更便宜点就好了！

评分☆☆☆☆☆

买houhuile，houhuile

评分☆☆☆☆☆

买houhuile，houhuile

评分☆☆☆☆☆

书很薄，价格很贵，内容不简单……

评分☆☆☆☆☆

不过还是有一定难度的。

评分☆☆☆☆☆

书还不错。应用方面看了一下，感觉大多是列举了现有的一些方案，并没有深入地分析随机矩阵理论的应用原理；推导分析过程也不够丰富。

评分☆☆☆☆☆

非常经典的书 很受启发

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