Eigenvalue Density of Correlated Complex Random Wishart Matrices

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