Eigenvalue Density of Correlated Complex Random Wishart Matrices

Physics – Mathematical Physics

Scientific paper

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Scientific paper

10.1103/PhysRevE.69.065101

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called ``correlated Wishart matrices'' occur in many fields ranging from information theory to multivariate analysis.

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