Universality in complex Wishart ensembles for general covariance matrices with 2 distinct eigenvalues

We considered N×NN×N Wishart ensembles in the class WC(ΣN,M)WC(ΣN,M) (complex Wishart matrices with MM degrees of freedom and covariance matrix ΣNΣN) such that N0N0 eigenvalues of ΣNΣN are 1 and N1=N−N0N1=N−N0 of them are aa. We studied the limit as MM, NN, N0N0 and N1N1 all go to infinity such that NM→c, N1N→β and 0