191 citations · 1.7k across the 93 of their papers we have counts for
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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…
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…
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…
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…
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…
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…
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…
Universality of local spectral statistics of products of random matrices
Gernot Akemann, Zdzislaw Burda, Mario Kieburg
We derive exact analytical expressions for correlation functions of singular values of the product of Ginibre matrices of size in the double scaling limit $M,N\rightarrow \…
Derivative principles for invariant ensembles
Mario Kieburg, Jiyuan Zhang
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other…
Universal eigenvector correlations in quaternionic Ginibre ensembles
Gernot Akemann, Yanik-Pascal Förster, Mario Kieburg
Non-Hermitian random matrices enjoy non-trivial correlations in the statistics of their eigenvectors. We study the overlap among left and right eigenvectors in Ginibre ensembles wi…
Harmonic analysis for rank-1 Randomised Horn Problems
Jiyuan Zhang, Mario Kieburg, Peter J. Forrester
The randomised Horn problem, in both its additive and multiplicative version, has recently drawn increasing interest. Especially, closed analytical results have been found for the…
Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality
Taro Nagao, Gernot Akemann, Mario Kieburg +1
We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse, due to a hard wall constraint, and are subject to an additional external…
From Integrable to Chaotic Systems: Universal Local Statistics of Lyapunov exponents
Gernot Akemann, Zdzislaw Burda, Mario Kieburg
Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with…
Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
Gernot Akemann, Mario Kieburg, Adam Mielke +1
We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian ort…
GUE-chGUE Transition preserving Chirality at finite Matrix Size
Takuya Kanazawa, Mario Kieburg
We study a random matrix model which interpolates between the the singular values of the Gaussian unitary ensemble (GUE) and of the chiral Gaussian unitary ensemble (chGUE). This s…
Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances
Gernot Akemann, Tomasz Checinski, Mario Kieburg
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory en…
Asymptotic Coincidence of the Statistics for Degenerate and Non-Degenerate Correlated Real Wishart Ensembles
Tim Wirtz, Mario Kieburg, Thomas Guhr
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, p…
Supersymmetry for Products of Random Matrices
Mario Kieburg
We consider the singular value statistics of products of independent random matrices. In particular we compute the corresponding averages of products of characteristic polynomials.…
The Smallest Eigenvalue Distribution in the Real Wishart-Laguerre Ensemble with Even Topology
Tim Wirtz, Gernot Akemann, Thomas Guhr +2
We consider rectangular random matrices of size belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble app…
Relating the Bures measure to the Cauchy two-matrix model
Peter J. Forrester, Mario Kieburg
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 and the…
Limiting Statistics of the Largest and Smallest Eigenvalues in the Correlated Wishart Model
Tim Wirtz, Mario Kieburg, Thomas Guhr
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the em…