Eigenvalue Density of the Doubly Correlated Wishart Model: Exact Results

Abstract

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density of the Wishart correlation matrices using supersymmetry. In the complex case we obtain a new closed form expression which we compare to previous results in the literature. In the more relevant and much more complicated real case we derive an expression for the density in terms of a fourfold integral. Finally, we calculate the density in the limit of large correlation matrices.

16 pages, 3 figures

References in corpus (5)

• Superbosonization of invariant random matrix ensembles
• Arbitrary Rotation Invariant Random Matrix Ensembles and Supersymmetry
• On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model

Cited by in corpus (1)

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