Journal article

Products of random matrices from polynomial ensembles

Mario Kieburg, Holger Koesters

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | INST MATHEMATICAL STATISTICS | Published : 2019

Abstract

Very recently we have shown that the spherical transform is a convenient tool for studying the relation between the joint density of the singular values and that of the eigenvalues for bi-unitarily invariant random matrices. In the present work we discuss the implications of these results for products of random matrices. In particular, we derive a transformation formula for the joint densities of a product of two independent bi-unitarily invariant random matrices, the first from a polynomial ensemble and the second from a polynomial ensemble of derivative type. This allows us to re-derive and generalize a number of recent results in random matrix theory, including a transformation formula fo..

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University of Melbourne Researchers

Grants

Awarded by Deutsche Forschungsgemeinschaft


Funding Acknowledgements

We thank Gernot Akemann and Friedrich Gotze for fruitful discussions. Moreover we acknowledge financial support by the CRC 701: "Spectral Structures and Topological Methods in Mathematics" of the Deutsche Forschungsgemeinschaft.