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


  • Mauro Politi
  • Enrico Scalas
  • Daniel Fulger
  • Guido Germano


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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  • Mauro Politi & Enrico Scalas & Daniel Fulger & Guido Germano, 2009. "Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation," Papers 0903.1629,
  • Handle: RePEc:arx:papers:0903.1629

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    References listed on IDEAS

    1. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
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