Tom Claeys

Biorthogonal ensembles of derivative type

I will introduce a class of biorthogonal ensembles on the real line with a specific derivative structure and show that they admit an explicit correlation kernel of double contour integral form. This correlation kernel is a valuable starting point for asymptotic analysis. We will demonstrate this by proving that two new classes of limit kernels can occur in these ensembles. The first type arises in biorthogonal ensembles describing the eigenvalues of the sum of two random matrices, while the second type arises for Muttalib-Borodin type deformations of polynomial ensembles.