| 《大维随机矩阵的谱分析(英文版)(第2版)》是由科学出版社出版的。 |
| Zhidong Bai is a professor of the School of Mathematics and Statistics at Northeast Normal University and Department of Statistics and Applied Probability at National University of Singapore. He is a Fellow of the Third World Academy of Sciences and a Fellow of the Institute of Mathematical Statistics. Jack W. Silverstein is a professor in the Department of Mathematics at North Carolina State University. He is a Fellow of the Institute of Mathematical Statistics. |
| preface to the second edition preface to the first edition 1 introduction 1.1 large dimensional data analysis 1.2 random matrix theory 1.3 methodologies 2 wigner matrices and semicircular law 2.1 semicircular law by the moment method 2.2 generalizations to the non-iid case 2.3 semicircular law by stieltjes transform 3 sample covariance matrices and the marcenko-pastur law 3.1 m-p law for the iid case 3.2 generalization to the non-iid case 3.3 proof of theorem 3.10 by the stieltjes transform 4 product of two random matrices 4.1 main:results 4.2 some graph theory and combinatorial results 4.3 proof df'theorem 4.1 4.4 lsd of the f-matrix 4.5 proof of theorems4:3 5 limits of extreme eigenvalues 5.1 limit of extreme eigenvalues of the wigner matrix 5.2 limits,of extreme eigenvalues of the sample covariance matrix 5.3 miscellanies 6 spectrum separation 6.1 what is spectrum separation? 6.2 proof of(1) 6.3 proof of(2) 6.4 proof of(3) 7 semicircular law for hadamsrd products 7.1 sparse matrix and hadamard product 7.2 truncation and normalization 7.3 proof of theorem 7.1 by the moment approach 8 convergence rates of esd 8.1 convergence rates of the expected esd of wigner matrices 8.2 further extensions 8.3 convergence rates of the expected esd of sample covariance matrices 8.4 some elementary calculus 8.5 rates of convergence in probability and almost surely 9 clt for linear spectral statistics 9.1 motivation and strategy 9.2 clt of lss for the wigner matrix 9.3 convergence of the process mn-emn 9.4 computation of tim mean and covauce function of g(f) 9.5 application to linear spectral statistics and related results 9.6 technical lemmas 9.7 clt of the lss for sample covariance matrices 9.8 convergence of stieltjes transforms 9.9 convergence of finite-dimensional distributions 9.10 tightness of mi(z) 9.11 convergence of mn2(z) 9.12 some derivations and calculations 9.13 clt for the f-matrix 9.14 proof of theorem 9.14 9.15 clt for the lss of a large dimensional beta-matrix 9.16 some examples 10 eigenvectors of sample covariance matrices 10.1 formulation and conjectures 10.2 a necessary condition for property 5' 10.3 moments of xp(fsp) 10.4 an example of weak convergence 10.5 extension of (10.2.6) to bn= t1/2spt1/2 10.6 proof of theorem 10.16 10.7 proof of theorem 10.21 10.8 proof of theorem 10.23 11 circular law 11.1 the problem and difficulty 11.2 a theorem establishing a partial answer to the circular law 11.3 lemmas on integral range reduction 11.4 characterization of the circular law 11.5 a rough rate on the convergence of vn(x, z) 11.6 proofs of (11.2.3) and (11.2.4) 11.7 proof of theorem 11.4 11.8 comments and extensions 11.9 some elementary mathematics 11.10 new developments 12 some applications of rmt 12.1 wireless communications 12.2 addlication to finance a some results in linear algebra a.1 inverse matrices and resolvent a.2 inequalities involving spectral distributions a.3 hadamard product and odot product a.4 extensions of singular-value inequalities a.5 perturbation inequalities a.6 rank inequalities a.7 a norm inequality b miscellanies b.1 moment convergence theorem b.2 stieltjes transform b.3 some lemmas about integrals of stieltjes transforms b.4 a lemma on the strong law of large numbers b.5 a lemma on quadratic forms relevant literature index |
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