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• W3100797907 abstract "We consider an ensemble of large non-Hermitian random matrices of the form $hat{H}+ihat{A}_s$, where $hat{H}$ and $hat{A}_s$ are Hermitian statistically independent random $Ntimes N$ matrices. We demonstrate the existence of a new nontrivial regime of weak non-Hermiticity characterized by the condition that the average of $Nmbox{Tr} hat{A}_s^2$ is of the same order as that of $mbox{Tr} hat{H}^2 $ when $Nto infty$. We find explicitly the density of complex eigenvalues for this regime in the limit of infinite matrix dimension. The density determines the eigenvalue distribution in the crossover regime between random Hermitian matrices whose real eigenvalues are distributed according to the Wigner semi-circle law and random complex matrices whose eigenvalues are distributed in the complex plane according to the so-called ``elliptic law''." @default.
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• W3100797907 date "1997-02-01" @default.
• W3100797907 modified "2023-09-23" @default.
• W3100797907 title "Almost-Hermitian random matrices: eigenvalue density in the complex plane" @default.
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• W3100797907 doi "https://doi.org/10.1016/s0375-9601(96)00904-8" @default.
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