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arXiv · 1706.08343

Location of the spectrum of Kronecker random matrices

Johannes Alt·Laszlo Erdos·Torben Krüger·Yuriy Nemish
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Abstract

For a general class of large non-Hermitian random block matrices $\mathbf{X}$ we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of $\mathbf{X}$ as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from [arXiv:1604.08188v4] offers a unified treatment of many structured matrix ensembles.

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Johannes Alt, Laszlo Erdos, Torben Krüger, Yuriy Nemish. 2017-06-26. Location of the spectrum of Kronecker random matrices. https://arxiv.org/abs/1706.08343

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