Random matrix approach to multivariate correlations: some limiting cases.
Recent advances have shown that the empirical correlation matrices of dynamical systems can be modeled as random matrices, for most part, chosen from an appropriate ensemble of the random matrix theory (RMT). In this work, we study certain limiting cases where this approach could potentially break down. Using a combination of analytical and numerical tools, we especially study the eigenvalue density and its spacing distribution. We show that the correlation matrices obtained from multivariate spatiotemporal timeseries, in a regime of spatiotemporal chaos, lead to strong deviations from RMT. We illustrate the results with time-series data drawn from coupled map lattices. We also explore the transition to the RMT regime from the limiting cases.
Santhanam
M S
MS
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden 01187, Germany.
Kantz
Holger
H