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math-ph2023★ 13 cited
Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
Gernot Akemann, Sung-Soo Byun, Markus Ebke +1
In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius in all three Ginibre ensembles. We determine the mean and varian…
math-ph2022★ 15 cited
Universality of the number variance in rotational invariant two-dimensional Coulomb gases
Gernot Akemann, Sung-Soo Byun, Markus Ebke
An exact map was established by Lacroix-A-Chez-Toine, Majumdar, and Schehr in [44] between the complex eigenvalues of complex non-Hermitian random matrices from the Ginibre ens…
math-ph2021★ 17 cited
Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
Gernot Akemann, Markus Ebke, Iván Parra
Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. These point processes are characterised by a matrix value…