Singular value correlation functions for products of Wishart random matrices

G Akemann, M Kieburg, L Wei - Journal of Physics A …, 2013‏ - iopscience.iop.org
We consider the product of M quadratic random matrices with complex elements and no
further symmetry, where all matrix elements of each factor have a Gaussian distribution. This …

Weak commutation relations and eigenvalue statistics for products of rectangular random matrices

JR Ipsen, M Kieburg - Physical Review E, 2014‏ - APS
We study the joint probability density of the eigenvalues of a product of rectangular real,
complex, or quaternion random matrices in a unified way. The random matrices are …

Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics

G Akemann, N Aygün, M Kieburg, P Päßler - arxiv preprint arxiv …, 2024‏ - arxiv.org
Recently, a conjecture about the local bulk statistics of complex eigenvalues has been made
based on numerics. It claims that there are only three universality classes, which have all …

Relating the Bures measure to the Cauchy two-matrix model

PJ Forrester, M Kieburg - Communications in Mathematical Physics, 2016‏ - Springer
The Bures metric is a natural choice in measuring the distance of density operators
representing states in quantum mechanics. In the past few years a random matrix ensemble …

On the distribution of the maximum value of the characteristic polynomial of GUE random matrices

YV Fyodorov, NJ Simm - Nonlinearity, 2016‏ - iopscience.iop.org
On the distribution of the maximum value of the characteristic polynomial of GUE random
matrices Page 1 Nonlinearity PAPER • OPEN ACCESS On the distribution of the maximum …

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 …

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 …

[HTML][HTML] Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence

N Hahn, M Kieburg, O Gat, T Guhr - Journal of Mathematical Physics, 2023‏ - pubs.aip.org
Topological invariance is a powerful concept in different branches of physics as they are
particularly robust under perturbations. We generalize the ideas of computing the statistics of …

[HTML][HTML] Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case

N Hahn, M Kieburg, O Gat, T Guhr - Journal of Mathematical Physics, 2023‏ - pubs.aip.org
We extend our recent study of winding number density statistics in Gaussian random matrix
ensembles of the chiral unitary (AIII) and chiral symplectic (CII) classes. Here, we consider …

Spectral properties of the Wilson-Dirac operator and random matrix theory

M Kieburg, JJM Verbaarschot, S Zafeiropoulos - Physical Review D—Particles …, 2013‏ - APS
Random matrix theory has been successfully applied to lattice quantum chromodynamics. In
particular, a great deal of progress has been made on the understanding, numerically as …