PUB - Publikationen an der Universität Bielefeld

We consider the singular value statistics of products of independent random matrices. In particular, we compute the corresponding averages of products of characteristic polynomials. To this aim, we apply the projection formula recently introduced for chiral random matrix ensembles which serves as a shortcut of the supersymmetry method. The projection formula enables us to study the local statistics where free probability currently fails. To illustrate the projection formula and underlining the power of our approach, we calculate the hard edge scaling limit of the Meijer G-ensembles comprising the Wishart-Laguerre (chiral Gaussian), the Jacobi (truncated orthogonal, unitary or unitary symplectic) and the Cauchy-Lorentz (heavy tail) random matrix ensembles. All calculations are done for real, complex, and quaternion matrices in a unifying way. In the case of real and quaternion matrices, the results are completely new and hint to the universality of the hard edge scaling limit for a product of these matrices, too. Moreover, we identify the non-linear sigma-models to the local statistics of product matrices at the hard edge.