Cipolloni Giorgio, Erdős László, Schröder Dominik
IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
Institute for Theoretical Studies, ETH Zurich, Clausiusstr. 47, 8092 Zurich, Switzerland.
Probab Theory Relat Fields. 2021;179(1):1-28. doi: 10.1007/s00440-020-01003-7. Epub 2020 Sep 25.
We consider large non-Hermitian real or complex random matrices 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 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.
我们考虑具有独立同分布中心元素的大型非厄米实或复随机矩阵。我们证明，它们在谱边缘（单位圆）附近的局部特征值统计与 Ginibre 系综的统计结果一致，即当矩阵元素为高斯分布时。这一结果是维格纳系综谱边缘处 Tracy-Widom 分布普遍性的非厄米对应物。
