Progress on the study of the Ginibre ensembles I: GinUE

SS Byun, PJ Forrester - arxiv preprint arxiv:2211.16223, 2022‏ - arxiv.org
The Ginibre unitary ensemble (GinUE) consists of $ N\times N $ random matrices with
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …

[كتاب][B] Progress on the Study of the Ginibre Ensembles

SS Byun, PJ Forrester - 2025‏ - library.oapen.org
This open access book focuses on the Ginibre ensembles that are non-Hermitian random
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …

Limits and fluctuations of p-adic random matrix products

R Van Peski - Selecta Mathematica, 2021‏ - Springer
We show that singular numbers (also known as elementary divisors, invariant factors or
Smith normal forms) of products and corners of random matrices over Q _p Q p are …

From integrable to chaotic systems: Universal local statistics of Lyapunov exponents

G Akemann, Z Burda, M Kieburg - Europhysics Letters, 2019‏ - iopscience.iop.org
From integrable to chaotic systems: Universal local statistics of Lyapunov exponents -
IOPscience Skip to content IOP Science home Accessibility Help Search Journals Journals list …

Gaussian fluctuations for products of random matrices

V Gorin, Y Sun - American Journal of Mathematics, 2022‏ - muse.jhu.edu
We study global fluctuations for singular values of $ M $-fold products of several right-
unitarily invariant $ N\times N $ random matrix ensembles. As $ N\to\infty $, we show the …

Exact relation between singular value and eigenvalue statistics

M Kieburg, H Kösters - Random Matrices: Theory and Applications, 2016‏ - World Scientific
We use classical results from harmonic analysis on matrix spaces to investigate the relation
between the joint densities of the singular values and the eigenvalues for complex random …

Universality of local spectral statistics of products of random matrices

G Akemann, Z Burda, M Kieburg - Physical Review E, 2020‏ - APS
We derive exact analytical expressions for correlation functions of singular values of the
product of M Ginibre matrices of size N in the double scaling limit M, N→∞. The singular …

Correlation functions between singular values and eigenvalues

M Allard, M Kieburg - arxiv preprint arxiv:2403.19157, 2024‏ - arxiv.org
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 size …

Polynomial ensembles and Pólya frequency functions

YP Förster, M Kieburg, H Kösters - Journal of Theoretical Probability, 2021‏ - Springer
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 …

Harmonic analysis for rank-1 randomised Horn problems

J Zhang, M Kieburg, PJ Forrester - Letters in Mathematical Physics, 2021‏ - Springer
The randomised Horn problem, in both its additive and multiplicative versions, has recently
drawn an increasing interest. Especially, closed analytical results have been found for the …