Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Random matrix approach to multivariate correlations: some limiting cases.

M S Santhanam1, Holger Kantz

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden 01187, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Extreme events of quantum walks on networks.

Physical review. E·2026
Same author

Statistical inference on specifying regression models for detecting dependence in autocorrelated series.

Physical review. E·2026
Same author

Transient times and cycle-rich topology in reservoir computing.

Chaos (Woodbury, N.Y.)·2026
Same author

Superstable geometry in triadic percolation.

Physical review. E·2026
Same author

Flux-fluctuation relation for quantum walks on networks.

Physical review. E·2026
Same author

Congestion and extreme events in urban street networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

This study reveals that random matrix theory (RMT) may fail for dynamical systems exhibiting spatiotemporal chaos. Correlation matrices deviate from RMT predictions, particularly in eigenvalue distributions.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Time Series Analysis

Background:

  • Empirical correlation matrices of dynamical systems are often modeled using random matrix theory (RMT).
  • This approach assumes matrices are drawn from specific random matrix ensembles.
  • The validity of this RMT approach in all dynamical regimes is not fully established.

Purpose of the Study:

  • To investigate the limitations of random matrix theory (RMT) in modeling correlation matrices.
  • To analyze eigenvalue density and spacing distributions in specific dynamical systems.
  • To explore conditions under which the RMT approach may break down.

Main Methods:

  • Utilized a combination of analytical and numerical techniques.
  • Examined multivariate spatiotemporal time series data.

Related Experiment Videos

  • Employed coupled map lattices as a model system.

    • Main Results:

    • Demonstrated significant deviations from RMT predictions for correlation matrices in spatiotemporal chaos.
    • Observed altered eigenvalue density and spacing distributions under these conditions.
    • Identified specific regimes where the RMT approximation is inadequate.

    Conclusions:

    • The application of random matrix theory to dynamical systems requires careful consideration of the system's regime.
    • Spatiotemporal chaos represents a limiting case where standard RMT models may not apply.
    • Further research is needed to understand transitions between RMT and non-RMT regimes.