35 citations · 176 across the 8 of their papers we have counts for
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The Interpolating Airy Kernels for the beta=1 and beta=4 Elliptic Ginibre Ensembles
G. Akemann, M. J. Phillips
We consider two families of non-Hermitian Gaussian random matrices, namely the elliptical Ginibre ensembles of asymmetric N-by-N matrices with Dyson index beta=1 (real elements) an…
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…
Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices
G. Akemann, M. Kieburg, M. J. Phillips
We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integra…
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…
Characteristic polynomials in real Ginibre ensembles
G. Akemann, M. J. Phillips, H. -J. Sommers
We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms th…