191 citations · 1.7k across the 93 of their papers we have counts for
96 papers
Winding Number Statistics of a Parametric Chiral Symplectic Random Matrix Ensemble
Pascal Toschka, Luke Haas, Thomas Guhr +2
The winding number is a simple topological invariant. In the case of chiral symmetry it characterises gapped phases of Fermions. We study statistical properties of this topological…
Quantum chaotic systems: a random-matrix approach
Mario Kieburg
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random…
Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory
Gernot Akemann, Georg Angermann, Mario Kieburg +1
Explicit expressions are proven for derivatives of the ratio of a determinant or Pfaffian determinant and a Vandermonde determinant. Such ratios appear for example in general group…
Universality of order statistics for Brownian reshuffling
Zdzislaw Burda, Mario Kieburg, Tomasz Maciocha
We discuss the order statistics of the particle positions of a gas of identical independent particles performing Brownian motion in one dimension in a potential that asymptotic…
Random matrix prediction of average entanglement entropy in non-Abelian symmetry sectors
Anwesha Chakraborty, Lucas Hackl, Mario Kieburg
We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global symmetry, constrained to fixed total spin $…
Average Winding Number for Determinantal Curves associated with 2-Matrix Models in the Class AIII
Mathieu Yahiaoui, Mario Kieburg
To classify one-dimensional disordered quantum systems with chiral symmetry, we analyse the winding number of the determinant of a parametrized non-Hermitian random matrix field ov…
Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble
Erik Aurell, Lucas Hackl, Mario Kieburg
We consider ensembles of pure Gaussian states parametrized by single-mode marginals and (optionally) specific mode-mode correlations. Such ensembles provide a model for the final s…
Universality of Top Rank Statistics for Brownian Reshuffling
Zdzislaw Burda, Mario Kieburg
We study the dynamical aspects of the top rank statistics of particles, performing Brownian motions on a half-line, which are ranked by their distance from the origin. For this pur…
Average mutual information for random fermionic Gaussian quantum states
Lucas Hackl, Mario Kieburg, Joel Maldonado
Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics,…
Yang-Lee zeros for real-space condensation
Zdzislaw Burda, Desmond A. Johnston, Mario Kieburg
Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-spac…
Winding Number Statistics for Chiral Random Matrices: Universal Correlations and Statistical Moments in the Unitary Case
Nico Hahn, Mario Kieburg, Omri Gat +1
The winding number is the topological invariant that classifies chiral symmetric Hamiltonians with one-dimensional parametric dependence. In this work we complete our study of the…
Complex symmetric, self-dual, and Ginibre random matrices: Analytical results for three classes of bulk and edge statistics
Gernot Akemann, Noah Aygün, Mario Kieburg +1
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…
Orthogonal polynomials in the normal matrix model with two insertions
Mario Kieburg, Arno B. J. Kuijlaars, Sampad Lahiry
We consider orthogonal polynomials with respect to the weight in the whole complex plane. We obtain strong asymptotics and the limiting normalized zero…
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…
Random pure Gaussian states and Hawking radiation
Erik Aurell, Lucas Hackl, Paweł Horodecki +2
A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum…
Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Parametric Determinants in the Orthogonal Case
Nico Hahn, Mario Kieburg, Omri Gat +1
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 consi…
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…
Winding Number Statistics for Chiral Random Matrices: Averaging Ratios of Determinants with Parametric Dependence
Nico Hahn, Mario Kieburg, Omri Gat +1
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 statisti…
Dip-ramp-plateau for Dyson Brownian motion from the identity on
Peter J. Forrester, Mario Kieburg, Shi-Hao Li +1
In a recent work the present authors have shown that the eigenvalue probability density function for Dyson Brownian motion from the identity on is an example of a newly iden…
Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
G. Akemann, V. Gorski, M. Kieburg
The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecut…
Volume-law entanglement entropy of typical pure quantum states
Eugenio Bianchi, Lucas Hackl, Mario Kieburg +2
The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability.…
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…
The Page Curve for Fermionic Gaussian States
Eugenio Bianchi, Lucas Hackl, Mario Kieburg
In a seminal paper, Page found the exact formula for the average entanglement entropy for a pure random state. We consider the analogous problem for the ensemble of pure fermionic…
Local Tail Statistics of Heavy-Tailed Random Matrix Ensembles with Unitary Invariance
Mario Kieburg, Adam Monteleone
We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigenvector statistics are decoupled. The motivating qu…