A First Course in Random Matrix Theory 1108488080, 9781108488082
The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data
313 54 4MB
English Pages [371] Year 2020
Table of contents :
Cover
Title Page
Copyright
Contents
Preface
Symbols
Part I - Classical Random Matrix Theory
1. Deterministic Matrices
2. Wigner Ensemble and Semi-Circle Law
3. More on Gaussian Matrices*
4. Wishart Ensemble and Marcenko–Pastur Distribution
5. Joint Distribution of Eigenvalues
6. Eigenvalues and Orthogonal Polynomials*
7. The Jacobi Ensemble*
Part II - Sums and Products of Random Matrices
8. Addition of Random Variables and Brownian Motion
9. Dyson Brownian Motion
10. Addition of Large Random Matrices
11. Free Probabilities
12. Free Random Matrices
13. The Replica Method*
14. Edge Eigenvalues and Outliers
Part III - Applications
15. Addition and Multiplication: Recipes and Examples
16. Products of Many Random Matrices
17. Sample Covariance Matrices
18. Bayesian Estimation
19. Eigenvector Overlaps and Rotationally Invariant Estimators
20. Applications to Finance
Appendix - Mathematical Tools
Index
Cover
Title Page
Copyright
Contents
Preface
Symbols
Part I - Classical Random Matrix Theory
1. Deterministic Matrices
2. Wigner Ensemble and Semi-Circle Law
3. More on Gaussian Matrices*
4. Wishart Ensemble and Marcenko–Pastur Distribution
5. Joint Distribution of Eigenvalues
6. Eigenvalues and Orthogonal Polynomials*
7. The Jacobi Ensemble*
Part II - Sums and Products of Random Matrices
8. Addition of Random Variables and Brownian Motion
9. Dyson Brownian Motion
10. Addition of Large Random Matrices
11. Free Probabilities
12. Free Random Matrices
13. The Replica Method*
14. Edge Eigenvalues and Outliers
Part III - Applications
15. Addition and Multiplication: Recipes and Examples
16. Products of Many Random Matrices
17. Sample Covariance Matrices
18. Bayesian Estimation
19. Eigenvector Overlaps and Rotationally Invariant Estimators
20. Applications to Finance
Appendix - Mathematical Tools
Index
- Author / Uploaded
- Marc Potters
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