Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble

Akemann G, Cikovic M, Venker M (2018)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 362(3): 1111-1141.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We consider non-Gaussian extensions of the elliptic Ginibre ensemble of complex non-Hermitian random matrices by fixing the trace Tr(XX (*)) of the matrix X with a hard or soft constraint. These ensembles have correlated matrix entries and non-determinantal joint densities of the complex eigenvalues. We study global and local bulk statistics in these ensembles, in particular in the limit of weak non-Hermiticity introduced by Fyodorov, Khoruzhenko and Sommers. Here, the support of the limiting measure collapses to the real line. This limit was motivated by physics applications and interpolates between the celebrated sine and Ginibre kernel. Our results constitute a first proof of universality of the interpolating kernel. Furthermore, in the limit of strong non-Hermiticity, where the support of the limiting measure remains an ellipse, we obtain local Ginibre statistics in the bulk of the spectrum.
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COMMUNICATIONS IN MATHEMATICAL PHYSICS
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362
Zeitschriftennummer
3
Seite
1111-1141
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Akemann G, Cikovic M, Venker M. Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2018;362(3):1111-1141.
Akemann, G., Cikovic, M., & Venker, M. (2018). Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 362(3), 1111-1141. doi:10.1007/s00220-018-3201-1
Akemann, G., Cikovic, M., and Venker, M. (2018). Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble. COMMUNICATIONS IN MATHEMATICAL PHYSICS 362, 1111-1141.
Akemann, G., Cikovic, M., & Venker, M., 2018. Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 362(3), p 1111-1141.
G. Akemann, M. Cikovic, and M. Venker, “Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 362, 2018, pp. 1111-1141.
Akemann, G., Cikovic, M., Venker, M.: Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 362, 1111-1141 (2018).
Akemann, Gernot, Cikovic, Milan, and Venker, Martin. “Universality at Weak and Strong Non-Hermiticity Beyond the Elliptic Ginibre Ensemble”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 362.3 (2018): 1111-1141.

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arXiv: arXiv:1610.06517

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