Polynomial Ensembles and Polya Frequency Functions

Foerster Y-P, Kieburg M, Kösters H (2020)
Journal of Theoretical Probability.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Foerster, Yanik-Pascal; Kieburg, Mario; Kösters, HolgerUniBi
Abstract / Bemerkung
We study several kinds of polynomial ensembles of derivative type which we propose to call Polya 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 Polya ensembles as well as convolutions with the more general class of polynomial ensembles. Moreover, we derive some general identities for group integrals similar to the Harish-Chandra-Itzykson-Zuber integral, and we relate Polya ensembles to Polya frequency functions. For illustration, we give a number of explicit examples for our results.
Stichworte
Probability measures on matrix spaces; Sums and products of independent; random matrices; Polynomial ensembles; Additive convolution; Multiplicative convolution; Polya frequency functions; Fourier; transform; Hankel transform; Spherical transform
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of Theoretical Probability
ISSN
0894-9840
eISSN
1572-9230
Page URI
https://pub.uni-bielefeld.de/record/2946131

Zitieren

Foerster Y-P, Kieburg M, Kösters H. Polynomial Ensembles and Polya Frequency Functions. Journal of Theoretical Probability. 2020.
Foerster, Y. - P., Kieburg, M., & Kösters, H. (2020). Polynomial Ensembles and Polya Frequency Functions. Journal of Theoretical Probability. doi:10.1007/s10959-020-01030-z
Foerster, Y. - P., Kieburg, M., and Kösters, H. (2020). Polynomial Ensembles and Polya Frequency Functions. Journal of Theoretical Probability.
Foerster, Y.-P., Kieburg, M., & Kösters, H., 2020. Polynomial Ensembles and Polya Frequency Functions. Journal of Theoretical Probability.
Y.-P. Foerster, M. Kieburg, and H. Kösters, “Polynomial Ensembles and Polya Frequency Functions”, Journal of Theoretical Probability, 2020.
Foerster, Y.-P., Kieburg, M., Kösters, H.: Polynomial Ensembles and Polya Frequency Functions. Journal of Theoretical Probability. (2020).
Foerster, Yanik-Pascal, Kieburg, Mario, and Kösters, Holger. “Polynomial Ensembles and Polya Frequency Functions”. Journal of Theoretical Probability (2020).

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