70 citations · 533 across the 26 of their papers we have counts for
27 papers
Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices
Gernot Akemann, Yan V. Fyodorov, Dmitry V. Savin
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-b…
Spectral moments of complex and symplectic non-Hermitian random matrices
Gernot Akemann, Sung-Soo Byun, Seungjoon Oh
We study non-Hermitian random matrices belonging to the symmetry classes of the complex and symplectic Ginibre ensemble, and present a unifying and systematic framework for analysi…
Logarithmic Spectral Distribution of a Non-Hermitian -Ensemble
Gernot Akemann, Francesco Mezzadri, Patricia Päßler +1
We introduce a non-Hermitian -ensemble and determine its spectral density in the limit of large and large matrix size . The ensemble is given by a general tridiagonal com…
The probability of almost all eigenvalues being real for the elliptic real Ginibre ensemble
Gernot Akemann, Sung-Soo Byun, Yong-Woo Lee
We investigate real eigenvalues of real elliptic Ginibre matrices of size , indexed by the parameter of asymmetry . In both the strongly and weakly non-Hermitian reg…
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…
Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking
G. Akemann, F. Balducci, A. Chenu +3
Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics when chaotic, or 2-dimensional (2d) Poisson statistics when…
Pfaffian structure of the eigenvector overlap for the symplectic Ginibre ensemble
Gernot Akemann, Sung-Soo Byun, Kohei Noda
We study the integrable structure and scaling limits of the conditioned eigenvector overlap of the symplectic Ginibre ensemble of Gaussian non-Hermitian random matrices with indepe…
Interactions Between Different Birds of Prey as a Random Point Process
Gernot Akemann, Nayden Chakarov, Oliver Krüger +3
The two-dimensional Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature . Based on previous work, it is proposed as a simple st…
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…
Universal microscopic spectrum of the unquenched QCD Dirac operator at finite temperature
Gernot Akemann, Tim R. Würfel
In the -regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theo…
Universality Conjecture for all Airy, Sine and Bessel Kernels in the Complex Plane
G. Akemann, M. J. Phillips
We address the question of how the celebrated universality of local correlations for the real eigenvalues of Hermitian random matrices of size NxN can be extended to complex eigenv…
Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
G. Akemann, P. H. Damgaard, K. Splittorff +1
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A gr…
Gap Probabilities in Non-Hermitian Random Matrix Theory
G. Akemann, M. J. Phillips, L. Shifrin
We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the G…
Matrix model correlation functions and lattice data for the QCD Dirac operator with chemical potential
G. Akemann, T. Wettig
We apply a complex chiral random matrix model as an effective model to QCD with a small chemical potential at zero temperature. In our model the correlation functions of complex ei…
The solution of a chiral random matrix model with complex eigenvalues
G. Akemann
We describe in detail the solution of the extension of the chiral Gaussian Unitary Ensemble (chGUE) into the complex plane. The correlation functions of the model are first calcula…
Microscopic correlation functions for the QCD Dirac operator with chemical potential
G. Akemann
A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation function…
New Critical Matrix Models and Generalized Universality
G. Akemann, G. Vernizzi
We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue den…
Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
G. Akemann
In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using…
QCD3 and the Replica Method
G. Akemann, D. Dalmazi, P. H. Damgaard +1
Using the replica method, we analyze the mass dependence of the QCD3 partition function in a parameter range where the leading contribution is from the zero momentum Goldstone fiel…
Macroscopic and Microscopic (Non-)Universality of Compact Support Random Matrix Theory
G. Akemann, G. Vernizzi
A random matrix model with a sigma-model like constraint, the restricted trace ensemble (RTE), is solved in the large-n limit. In the macroscopic limit the smooth connected two-poi…
Spectra of massive and massless QCD Dirac operators: A novel link
G. Akemann, E. Kanzieper
We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta=1,2, and 4) leads to emerge…
On Finite-Volume Gauge Theory Partition Functions
G. Akemann, P. H. Damgaard
We prove a Mahoux-Mehta--type theorem for finite-volume partition functions of SU(N_c\geq 3) gauge theories coupled to fermions in the fundamental representation. The large-volume…
Non-universality of compact support probability distributions in random matrix theory
G. Akemann, G. M. Cicuta, L. Molinari +1
The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with the one of the canonical Gaussian ens…
Multicritical Matrix Models and the Chiral Phase Transition
G. Akemann
Universality of multicritical unitary matrix models is shown and a new scaling behavior is found in the microscopic region of the spectrum, which may be relevant for the low energy…