Wigner matrices and semicircular law -- Sample covariance matrices and the Marc̆enko-Pastur law -- Product of two random matrices -- Limits of extreme Eigenvalues -- Spectrum separation -- Semicircular law for Hadamard products -- Convergence rates of ESD -- CLT for linear spectral statistics -- Eigenvectors of sample covariances matrices -- Circular law -- Some applications of RMT -- Some results in linear algebra -- Miscellanies
Summary
This text introduces basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. It focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science
