Eigenvalue density of empirical covariance matrix for correlated samples

Details Eigenvalue density of empirical covariance matrix for correlated samples Eigenvalue density of empirical covariance matrix for correlated samples

2005-08-19

arxiv.org/abs/cond-mat/0508451v1

Acta Phys. Pol. B36, 2641 (2005)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 5 figures, to appear in Acta Phys. Pol. B (Proceedings of the conference on `Applications of Random Matrix Theory to

Scientific paper

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. The method allows for exact determination of the experimental spectrum for a given covariance matrix and given correlations between samples in the limit of large N 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.

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