Spectral Moments of Correlated Wishart Matrices

We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral moments and the eigenvalue densities of the covariance matrices and their estimators. The results can be used in practice to extract information about the genuine correlations from the given experimental realization of random matrices.