Spectral densities of Wishart-Lévy free stable random matrices Analytical results and Monte Carlo validation
نویسندگان
چکیده
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 Lévy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Lévy stable random variables and validate it by Monte Carlo simulation. PACS. 89.65.Gh Economics; econophysics, financial markets, business and management – 02.50.Ng Distribution theory and Monte Carlo studies – 02.70.Uu Applications of Monte Carlo methods
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تاریخ انتشار 2009