A first course in random matrix theory for physicists, engineers and data scientists
The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the re...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2021
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Determine matrices
- Wigner ensemble and semi-circle law
- More on Gaussian matrices
- Wishart ensemble and Marcenko-Pastur distribution
- Joint distribution of eigenvalues
- Eigenvalues and Orthogonal polynomials
- The Jacobi ensemble
- Addition of random variables & Brownian motion
- Dyson Brownian motion
- Addition of large random matrices
- Free probabilities
- Free random matrices
- The replica method
- Edge eigenvalues and outliers
- Addition and multiplication : recipes and examples
- Products of many random matrices
- Sample covariance matrices
- Bayesian estimation
- Eigenvector overlaps and rotationally invariant estimators
- Applications to finance