Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices

Chapters in this book

1. Frontmatter I
2. CONTENTS V
3. List of basic notations and assumptions XVII
4. Preface and some historical remarks XX
5. Chapter 1. Introduction to the theory of sample matrices of fixed dimension 1
6. Chapter 2. Canonical equations 51
7. Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices 139
8. Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices 201
9. Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices 277
10. Chapter 6. The first proof of the Strong Circular Law 325
11. Chapter 7. Strong Law for normalized spectral functions of nonselfadjoint random matrices with independent row vectors and simple rigorous proof of the Strong Circular Law 349
12. Chapter 8. Rigorous proof of the Strong Elliptic Law 369
13. Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries 405
14. Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices 435
15. Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n_-1/2) 453
16. Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix Ȓm„(n) is equal to 0^(n-1/2) under the condition m„n^-1≤c<1 495
17. Chapter 13. The First Spacing Law for random symmetric matrices 535
18. Chapter 14. Ten years of General Statistical Analysis (The main G-estimators of General Statistical Analysis) 553
19. References 649
20. Index 669