Pseudo-Hermitian β-Laguerre Ensemble with Real Eigenvalues

It is shown how a rectangular Gaussian matrix of the Wishart matrices can be reduced to a bi-diagonal form using the Maximum Entropy Principle. The Hermitian β-Laguerre ensemble is then constructed by taking the product of the bi-diagonal by its adjoint. By resorting again to the MEP, the pseudo-Hermitian β-Laguerre ensemble is introduced. Once this is done, the occurrence of the 2β Dyson index effect in the pseudo-Hermitian β-Laguerre case is proved.