Marc Potters, Jean-Philippe Bouchaud

A First Course in Random Matrix Theory

• Gebundenes Buch

Produktbeschreibung

Classical statistical tools that handled real-life data have become inadequate upon the emergence of Big Data. Random matrix theory and free calculus introduced here present valuable solutions to the complex challenges posed by large datasets. Real world applications make it an essential tool for physicists, engineers, data analysts and economists.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 370
• Erscheinungstermin: 7. Januar 2021
• Englisch
• Abmessung: 253mm x 180mm x 27mm
• Gewicht: 874g
• ISBN-13: 9781108488082
• ISBN-10: 1108488080
• Artikelnr.: 60064257

Autorenporträt

Marc Potters is Chief Investment Officer of CFM, an investment firm based in Paris. Marc maintains strong links with academia and as an expert in Random Matrix Theory, he has taught at UCLA and Sorbonne University. He is co-author of Theory of Financial Risk and Derivative Pricing (Cambridge 2003).

Inhaltsangabe

Preface
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
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 A. Appendices: Mathematical Tools
List of Symbols
Index.