Recently Burkhardt et. al. introduced the k-checkerboard random matrix ensembles, which have a split limiting behavior of the eigenvalues (in the limit all but k of the eigenvalues are on the order of √ N and converge to semi-circular behavior, with the remaining k of size N 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.
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