Acta Physica Polonica B

Vol. 36, No. 9, September 2005, page 2641


Eigenvalue Density of Empirical Covariance Matrix for Correlated Samples

Z. Burda, J. Jurkiewicz, B. Waclaw

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. Görlich, 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 \rightarrow \infty 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.

PACS numbers: 02.50.--r, 02.60.--x, 89.90.+n



 
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