Introduced in 1928, many years before the celebrated Gaussian ensembles of Wigner-Dyson, the Wishart ensemble contains covariance matrices of a maximally random data set. The 'N' eigenvalues constitute a set of strongly correlated random variables, for which a number of analytical results (both for finite N and for N\to\infty) can be derived. In the first part, I will present general results and techniques, and give two examples of application: 1) spectral properties of financial data sets (and Marcenko-Pastur distribution). 2) random pure entangled states in a bipartite Hilbert space (and distribution of the smallest eigenvalue). In the second part, I concentrate on a recent result (large deviation of the maximum eigenvalue) and on some work in progress (superstatistical Wishart-Laguerre ensemble). I also point out the differences between spectral results on a global (macroscopic, non-universal), and local (microscopic, universal) scale.
Seminar on Disorder and Strong Correlations: "Wishart-Laguerre ensemble of Random Matrices"
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