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Spectral densities of Wishart-Lévy free stable random matrices

Analytical results and Monte Carlo validation

  • Topical Issue on Interdisciplinary Applications of Physics in Economics and Finance
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Abstract

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. Here the derivation of an analytical expression for the spectra of covariance matrices approximated by free Lévy stable random variables is reviewed comprehensively and validated by Monte Carlo simulation.

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Author information

Authors and Affiliations

  1. Department of Physics, University of Milan, via Giovanni Celoria 16, 20133, Milano, Italy

    M. Politi

  2. Department of Chemistry and WZMW, Computer Simulation Group, Philipps-University Marburg, 35032, Marburg, Germany

    M. Politi, D. Fulger & G. Germano

  3. Department of Advanced Sciences and Technology, Laboratory on Complex Systems, Amedeo Avogadro University of Eastern Piedmont, Viale Teresa Michel 11, 15121, Alessandria, Italy

    E. Scalas & D. Fulger

  4. Complex Systems Lagrange Lab, Institute for Scientific Interchange, Viale Settimio Severo 65, 10133, Torino, Italy

    D. Fulger

Authors
  1. M. Politi
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  2. E. Scalas
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  3. D. Fulger
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  4. G. Germano
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Correspondence to G. Germano.

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Politi, M., Scalas, E., Fulger, D. et al. Spectral densities of Wishart-Lévy free stable random matrices. Eur. Phys. J. B 73, 13–22 (2010). https://doi.org/10.1140/epjb/e2009-00360-7

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  • DOI: https://doi.org/10.1140/epjb/e2009-00360-7

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