Karhunen-Lo`eve Decomposition of Extensive Chaos
  We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f) needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length xi_KLD(f) to be defined that is easily calculated from spatially localized data. We show that xi_KLD(f) has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos. 
Scott M. Zoldi (Department of Physics, Center for Nonlinear,Complex   Systems, Duke University), Henry S. Greenside (Departm...