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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 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.

History

Publication status

  • Published

Journal

European Physical Journal B: Condensed Matter and Complex Systems

ISSN

1434-6028

Publisher

EDP Sciences

Issue

1

Volume

73

Page range

13-22

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-09-25

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