We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of $X$ are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.

中文翻译：

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非厄米随机矩阵的边普遍性

我们考虑具有独立、同分布的中心条目的大型非厄米实数或复数随机矩阵 $X$。我们证明了它们在谱边缘、单位圆附近的局部特征值统计与 Ginibre 系综的一致，即当 $X$ 的矩阵元素是高斯时。这个结果是 Wigner 系综光谱边缘的 Tracy-Widom 分布的普适性的非厄米对应。