Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

Details Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

2009-03-09

arxiv.org/abs/0903.1629v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure, submitted to Eur. Phys. J. B

Scientific paper

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 Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.

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