Spectral densities of Wishart-Levy free stable random matricesAnalytical results and Monte Carlo validation

摘要

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with L′evy stable distributions. Here the derivation of an analytical expression for the spectra of covariance matrices approximated by free L′evy stable random variables is reviewed comprehensively and validated by Monte Carlo simulation.