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A first course in random matrix theory : for physicists, engineers and data scientists /

Bibliographic Details
Main Authors: Potters, Marc, 1969- (Author), Bouchaud, Jean-Philippe, 1962- (Author)
Corporate Author: Cambridge University Press
Format: eBook
Language:English
Published: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021.
Subjects:
Random matrices.
Electronic books.
Online Access:Connect to the full text of this electronic book
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.