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Spectral densities of Wishart-Levy free stable random matrices
journal contribution
posted on 2023-06-08, 18:25 authored by M Politi, Enrico Scalas, D Fulger, G GermanoRandom 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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Publication status
- Published
Journal
European Physical Journal B: Condensed Matter and Complex SystemsISSN
1434-6028Publisher
EDP SciencesExternal DOI
Issue
1Volume
73Page range
13-22Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2014-09-25Usage metrics
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