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

Listed author(s):
  • 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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Paper provided by in its series Papers with number 0903.1629.

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Date of creation: Mar 2009
Publication status: Published in European Physical Journal B 79 (1), 13-22, 2010
Handle: RePEc:arx:papers:0903.1629
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