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Singular value correlation functions for products of Wishart random matrices
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 …
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, 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
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 …
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 …
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 …
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 …
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 …
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
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 …
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
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 …
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 …
particular, a great deal of progress has been made on the understanding, numerically as …