article published yes Johannes Alt author 36D3D8B6-F248-11E8-B48F-1D18A9856A87 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Torben H Krüger author 3020C786-F248-11E8-B48F-1D18A9856A870000-0002-4821-3297 Yuriy Nemish author 4D902E6A-F248-11E8-B48F-1D18A9856A870000-0002-7327-856X LaEr department Random matrices, universality and disordered quantum systems project 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. Institut Henri Poincaré2019 eng 0246-0203 1706.08343 00046779360000310.1214/18-AIHP894 552661-696 https://research-explorer.ista.ac.at/record/149 Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. 2019;55(2):661-696. doi:<a href="https://doi.org/10.1214/18-AIHP894">10.1214/18-AIHP894</a> Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:<a href="https://doi.org/10.1214/18-AIHP894">10.1214/18-AIHP894</a>. Alt, J., Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institut Henri Poincaré. <a href="https://doi.org/10.1214/18-AIHP894">https://doi.org/10.1214/18-AIHP894</a> J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019. Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institut Henri Poincaré, 2019. <a href="https://doi.org/10.1214/18-AIHP894">https://doi.org/10.1214/18-AIHP894</a>. J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 661–696. Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(2), 661–696. 62402019-04-08T14:05:04Z2026-07-08T06:17:16Z