Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble

Akemann G, Cikovic M, Venker M (2016)
arXiv:1610.06517.

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Abstract
We consider a non-Gaussian extension of the elliptic Ginibre ensemble of complex non-Hermitian random matrices by adding a trace squared term. This ensemble has correlated matrix entries and a non-determinantal joint density of eigenvalues. These features are absent in non-Hermitian Wigner type ensembles or normal random matrix ensembles with a potential. We provide a detailed analysis of the limit of weak non-Hermiticity introduced by Fyodorov, Khoruzhenko and Sommers, where the support of the limiting measure collapses to the real line. The limiting local correlations, however, extend to the complex plane, are determinantal, and interpolate between sine kernel and Ginibre statistics. In particular, this constitutes a first proof of universality for the interpolating kernel. Furthermore, in the limit of strong non-Hermiticity in the bulk of the spectrum, we recover Ginibre statistics from our ensemble as well, thus extending known universality results.
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Akemann G, Cikovic M, Venker M. Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble. arXiv:1610.06517. 2016.
Akemann, G., Cikovic, M., & Venker, M. (2016). Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble. arXiv:1610.06517
Akemann, G., Cikovic, M., and Venker, M. (2016). Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble. arXiv:1610.06517.
Akemann, G., Cikovic, M., & Venker, M., 2016. Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble. arXiv:1610.06517.
G. Akemann, M. Cikovic, and M. Venker, “Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble”, arXiv:1610.06517, 2016.
Akemann, G., Cikovic, M., Venker, M.: Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble. arXiv:1610.06517. (2016).
Akemann, Gernot, Cikovic, Milan, and Venker, Martin. “Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble”. arXiv:1610.06517 (2016).
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