Eigenvalue density of empirical covariance matrix for correlated samples

Z. Burda; J. Jurkiewicz; B. Waclaw

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Eigenvalue density of empirical covariance matrix for correlated samples

Z. Burda·J. Jurkiewicz·B. Waclaw

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Abstract

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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Z. Burda, J. Jurkiewicz, B. Waclaw. 2005-08-19. Eigenvalue density of empirical covariance matrix for correlated samples. https://arxiv.org/abs/cond-mat/0508451

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