PMID: 15244878Jul 13, 2004Paper

Random matrix approach to multivariate correlations: some limiting cases

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M S Santhanam, Holger Kantz

Abstract

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.

References

Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A D MirlinT H Seligman
Apr 16, 1990·Physical Review Letters·G CasatiF Izrailev
Jul 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M S Santhanam, P K Patra
Aug 11, 2001·Physical Review Letters·E CuevasM Ortuño
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P GopikrishnanH E Stanley
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A M Sengupta, P P Mitra
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vasiliki PlerouH Eugene Stanley
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marc BarthélemyEric Guichard

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Citations

Apr 8, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics· Vinayak, Akhilesh Pandey

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