A First Course in Random Matrix Theory: for Physicists, Engineers and Data Scientists

Marc Potters; Jean-Philippe Bouchaud

doi:10.1017/9781108768900

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A First Course in Random Matrix Theory

A First Course in Random Matrix Theory

for Physicists, Engineers and Data Scientists

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xiii

List of Symbols
pp xiv-xx

Part I - Classical Random Matrix Theory
pp 1-2

1 - Deterministic Matrices
pp 3-14

2 - Wigner Ensemble and Semi-Circle Law
pp 15-29

3 - More on Gaussian Matrices*
pp 30-42

4 - Wishart Ensemble and Marčenko–Pastur Distribution
pp 43-57

5 - Joint Distribution of Eigenvalues
pp 58-82

6 - Eigenvalues and Orthogonal Polynomials*
pp 83-96

7 - The Jacobi Ensemble*
pp 97-108

Part II - Sums and Products of Random Matrices
pp 109-110

8 - Addition of Random Variables and Brownian Motion
pp 111-120

9 - Dyson Brownian Motion
pp 121-135

10 - Addition of Large Random Matrices
pp 136-154

11 - Free Probabilities
pp 155-176

12 - Free Random Matrices
pp 177-198

13 - The Replica Method*
pp 199-219

14 - Edge Eigenvalues and Outliers
pp 220-240

Part III - Applications
pp 241-242

15 - Addition and Multiplication: Recipes and Examples
pp 243-256

16 - Products of Many Random Matrices
pp 257-266

17 - Sample Covariance Matrices
pp 267-280

18 - Bayesian Estimation
pp 281-296

19 - Eigenvector Overlaps and Rotationally Invariant Estimators
pp 297-320

20 - Applications to Finance
pp 321-338

Appendix - Mathematical Tools
pp 339-346

Index
pp 347-350