Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits (Q466038)

\textit{G. Akemann}, {J. R. Ipsen} and \textit{M. Kieburg} [``Products of rectangular random matrices: singular values and progressive scattering'', Phys. Rev. E 88, Article ID 052118, 13 p. (2013)] recently showed that the squared singular values of products of \(M\) rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation kernel that can be expressed in terms of Meijer \(G\)-functions. The authors show that this point process can be interpreted as a multiple orthogonal polynomial ensemble. They give integral representations for the relevant multiple orthogonal polynomials and a new double contour integral for the correlation kernel, which allows to find its scaling limits at the origin (hard edge). The limiting kernels generalize the classical Bessel kernels. For \(M=2\) they coincide with the scaling limits found by Bertola, Gekhtman, and Szmigielski [\textit{M. Bertola} et al., Commun. Math. Phys. 326, No. 1, 111--144 (2014; Zbl 1303.82018)] in the Cauchy--Laguerre two--matrix model, which indicates that these kernels represent a new universality class in random matrix theory.