Journal article

Polynomial Ensembles and Polya Frequency Functions

Yanik-Pascal Foerster, Mario Kieburg, Holger Koesters

JOURNAL OF THEORETICAL PROBABILITY | SPRINGER/PLENUM PUBLISHERS | Published : 2020

Abstract

We study several kinds of polynomial ensembles of derivative type which we propose to call Pólya ensembles. These ensembles are defined on the spaces of complex square, complex rectangular, Hermitian, Hermitian antisymmetric and Hermitian anti-self-dual matrices, and they have nice closure properties under the multiplicative convolution for the first class and under the additive convolution for the other classes. The cases of complex square matrices and Hermitian matrices were already studied in former works. One of our goals is to unify and generalize the ideas to the other classes of matrices. Here, we consider convolutions within the same class of Pólya ensembles as well as convolutions w..

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University of Melbourne Researchers

Grants

Awarded by Deutsche Forschungsgemeinschaft (DFG)


Funding Acknowledgements

We want to thank Gernot Akemann, Friedrich Gotze and Arno Kuijlaars for fruitful discussions on this topic. Moreover, we acknowledge support by CRC 701 "Spectral Structures and Topological Methods in Mathematics" as well as by grant AK35/2-1 "Products of Random Matrices", both funded by Deutsche Forschungsgemeinschaft (DFG). The work of Yanik-Pascal Forster was formerly supported by Studienstiftung des deutschen Volkes.