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

Random Matrix Theory and Cross-correlations in Global Financial Indices and Local Stock Market Indices