Location of the spectrum of Kronecker random matrices
For a general class of large non-Hermitian random block matrices 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 X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles.
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661-696
661-696
Institut Henri PoincarĂ©