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

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