  We investigate the hard edge scaling limit of the ensemble defined by the
squared singular values of the product of two coupled complex random matrices.
When taking the coupling parameter to be dependent on the size of the product
matrix, in a certain double scaling regime at the origin the two matrices
become strongly coupled and we obtain a new hard edge limiting kernel. It
interpolates between the classical Bessel-kernel describing the hard edge
scaling limit of the Laguerre ensemble of a single matrix, and the Meijer
G-kernel of Kuijlaars and Zhang describing the hard edge scaling limit for the
product of two independent Gaussian complex matrices. It differs from the
interpolating kernel of Borodin to which we compare as well.
