  We analyzed cross-correlations between price fluctuations of global financial
indices (20 daily stock indices over the world) and local indices (daily
indices of 200 companies in the Korean stock market) by using random matrix
theory (RMT). We compared eigenvalues and components of the largest and the
second largest eigenvectors of the cross-correlation matrix before, during, and
after the global financial the crisis in the year 2008. We find that the
majority of its eigenvalues fall within the RMT bounds [{\lambda}_,
{\lambda}+], where {\lambda}_- and {\lambda}_+ are the lower and the upper
bounds of the eigenvalues of random correlation matrices. The components of the
eigenvectors for the largest positive eigenvalues indicate the identical
financial market mode dominating the global and local indices. On the other
hand, the components of the eigenvector corresponding to the second largest
eigenvalue are positive and negative values alternatively. The components
before the crisis change sign during the crisis, and those during the crisis
change sign after the crisis. The largest inverse participation ratio (IPR)
corresponding to the smallest eigenvector is higher after the crisis than
during any other periods in the global and local indices. During the global
financial the crisis, the correlations among the global indices and among the
local stock indices are perturbed significantly. However, the correlations
between indices quickly recover the trends before the crisis.
