Cuprins
Frontmatter – CONTENTS – List of basic notations and assumptions – Preface and some historical remarks – Chapter 1. Introduction to the theory of sample matrices of fixed dimension – Chapter 2. Canonical equations – Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices – Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices – Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices – Chapter 6. The first proof of the Strong Circular Law – 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 – Chapter 8. Rigorous proof of the Strong Elliptic Law – Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries – Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices – Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n-1/2) – Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix ?m„(n) is equal to 0(n-1/2) under the condition m„n-1?c
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