Spectral density of autocorrelated Wishart-Levy matrices

Spectral properties of time-correlated Wishart-Levy matrices are studied. The correlation matrices are built from ensembles of time series obtained from a deterministic chaotic one-dimensional map with Cauchy distributed entries. Dependence of the spectral density on autocorrelations of the time series is investigated. Two basically different regimes of the spectra appear: extended states with small eigenvalues and localized states with high eigenvalues. Autocorrelations in the time series imply a decrease of the fraction of localized states as 1/(1+tau(0)), where tau(0) is the correlation time. For sufficiently large time correlations only extended states remain with eigenvalues clustered around zero.