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It has been shown that, if a model displays long-range (power-law) spatialcorrelations, its equal-time correlation matrix of this model will also have apower law tail in the distribution of its high-lying eigenvalues. The purposeof this letter is to show that the converse is generally incorrect: a power-lawtail in the high-lying eigenvalues of the correlation matrix may exist even inthe absence of equal-time power law correlations in the original model. We maytherefore view the study of the eigenvalue distribution of the correlationmatrix as a more powerful tool than the study of correlations, one which may infact uncover structure, that would otherwise not be apparent. Specifically, weshow that in the Totally Asymmetric Simple Exclusion Process, whereas there areno clearly visible correlations in the steady state, the eigenvalues of itscorrelation matrix exhibit a rich structure which we describe in detail.

Correlation Matrix Spectra: A Tool for Detecting Non-apparent Correlations?