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Spectral densities of Wishart-Lévy free stable random matrices

Politi, M; Scalas, E; Fulger, D; Germano, G; (2010) Spectral densities of Wishart-Lévy free stable random matrices. European Physical Journal B , 73 (1) pp. 13-22. 10.1140/epjb/e2009-00360-7. Green open access

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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.

Type: Article
Title: Spectral densities of Wishart-Lévy free stable random matrices
Open access status: An open access version is available from UCL Discovery
DOI: 10.1140/epjb/e2009-00360-7
Publisher version: http://dx.doi.org/10.1140/epjb/e2009-00360-7
Language: English
Additional information: The final publication is available at Springer via http://dx.doi.org/10.1140/epjb/e2009-00360-7.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1407446
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