191 citations · 1.7k across the 93 of their papers we have counts for
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Correlation functions between singular values and eigenvalues
Matthias Allard, Mario Kieburg
Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix…
A rate of convergence when generating stable invariant Hermitian random matrix ensembles
Mario Kieburg, Jiyuan Zhang
Recently, we have classified Hermitian random matrix ensembles that are invariant under the conjugate action of the unitary group and stable with respect to matrix addition. Apart…
Stable distributions and domains of attraction for unitarily invariant Hermitian random matrix ensembles
Mario Kieburg, Jiyuan Zhang
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action o…
Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics
Mario Kieburg, Shi-Hao Li, Jiyuan Zhang +1
The framework of spherical transforms and Pólya ensembles is of utility in deriving structured analytic results for sums and products of random matrices in a unified way. In the pr…
Products of Complex Rectangular and Hermitian Random Matrices
Mario Kieburg
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approac…
Hard Edge Statistics of Products of Pólya Ensembles and Shifted GUE's
Mario Kieburg
Very recently, we have shown how the harmonic analysis approach can be modified to deal with products of general Hermitian and complex random matrices at finite matrix dimension. I…
Multiplicative Convolution of Real Asymmetric and Real Antisymmetric Matrices
Mario Kieburg, Peter J. Forrester, Jesper R. Ipsen
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribut…
Additive Matrix Convolutions of Pólya Ensembles and Polynomial Ensembles
Mario Kieburg
Recently subclasses of polynomial ensembles for additive and multiplicative matrix convolutions were identified which were called Pólya ensembles (or polynomial ensembles of deriva…
Polynomial Ensembles and Pólya Frequency Functions
Yanik-Pascal Förster, Mario Kieburg, Holger Kösters
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 rec…
Singular value statistics of matrix products with truncated unitary matrices
Mario Kieburg, Arno B. J. Kuijlaars, Dries Stivigny
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result…