Free Lévy matrices and financial correlations

Zdzisław Burda, Jerzy Jurkiewicz, Maciej A. Nowak, Gabor Papp, Tsmail Zahed

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16 Citations (Scopus)


We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an appropriate choice of asymmetry and Lévy index (α/ 2 = 3/4) the free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market. Our results are of interest to a number of stochastic systems with power law noise.

Original languageEnglish
Pages (from-to)694-700
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-4
Publication statusPublished - Nov 15 2004



  • Correlation matrix
  • Eigenvalue spectrum
  • Random matrix theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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