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• W2004403712 abstract "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) and with beta=4 (quaternion-real elements). Both ensembles have already been solved for finite N using the method of skew-orthogonal polynomials, given for these particular ensembles in terms of Hermite polynomials in the complex plane. In this paper we investigate the microscopic weakly non-Hermitian large-N limit of each ensemble in the vicinity of the largest or smallest real eigenvalue. Specifically, we derive the limiting matrix-kernels for each case, from which all the eigenvalue correlation functions can be determined. We call these new kernels the interpolating Airy kernels, since we can recover -- as opposing limiting cases -- not only the well-known Airy kernels for the Hermitian ensembles, but also the complementary error function and Poisson kernels for the maximally non-Hermitian ensembles at the edge of the spectrum. Together with the known interpolating Airy kernel for beta=2, which we rederive here as well, this completes the analysis of all three elliptical Ginibre ensembles in the microscopic scaling limit at the spectral edge." @default.
• W2004403712 created "2016-06-24" @default.
• W2004403712 creator A5018741680 @default.
• W2004403712 creator A5079445757 @default.
• W2004403712 date "2014-03-21" @default.
• W2004403712 modified "2023-10-17" @default.
• W2004403712 title "The Interpolating Airy Kernels for the $$beta =1$$ β = 1 and $$beta =4$$ β = 4 Elliptic Ginibre Ensembles" @default.
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• W2004403712 doi "https://doi.org/10.1007/s10955-014-0962-6" @default.
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