Eigenvalue density of empirical covariance matrix for correlated samples

We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for uncorrelated samples (Z. Burda, A. Gorlich, J. Jurkiewicz, B. Waclaw, cond-mat/0508341). The method allows for exact determination of the experimental spectrum for a given covariance matrix and given correlations between samples in the limit N -> infinity and N/T = r = const with N being the number of degrees of freedom and T being the number of samples. We discuss the effect of correlations on several examples.