Recently Burkhardt et al. introduced the [Formula: see text]-checkerboard random matrix ensembles, which have a split limiting behavior of the eigenvalues (in the limit all but [Formula: see text] of the eigenvalues are on the order of [Formula: see text] and converge to semi-circular behavior, with the remaining [Formula: see text] of size [Formula: see text] and converging to hollow Gaussian ensembles). We generalize their work to consider non-Hermitian ensembles with complex eigenvalues; instead of a blip new behavior is seen, ranging from multiple satellites to annular rings. These results are based on moment method techniques adapted to the complex plane as well as analysis of singular values.

中文翻译：

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非厄米随机矩阵系综的谱统计

最近 Burkhardt 等人。介绍了[公式：见文本]-棋盘随机矩阵集合，它具有特征值的分裂限制行为（在极限中，除[公式：见文本]之外的所有特征值都在 [公式：见文本] 和收敛到半圆形行为，剩余的 [公式：见文本] 的大小 [公式：见文本] 并收敛到空心高斯集合）。我们将他们的工作推广到考虑具有复杂特征值的非厄米特系综；而不是一个昙花一现的新行为，从多颗卫星到环形环。这些结果基于适用于复平面的矩法技术以及奇异值分析。