{"abstract":[{"text":"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.","lang":"eng"}],"isi":1,"day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"publisher":"Institut Henri Poincaré","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"}]},"type":"journal_article","intvolume":"        55","title":"Location of the spectrum of Kronecker random matrices","oa":1,"quality_controlled":"1","external_id":{"isi":["000467793600003"],"arxiv":["1706.08343"]},"date_published":"2019-05-01T00:00:00Z","article_processing_charge":"No","doi":"10.1214/18-AIHP894","ec_funded":1,"citation":{"ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. <i>Annales de l’institut Henri Poincare</i>. 2019;55(2):661-696. doi:<a href=\"https://doi.org/10.1214/18-AIHP894\">10.1214/18-AIHP894</a>","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” <i>Annales de l’institut Henri Poincare</i>, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</i>. Institut Henri Poincaré, 2019. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</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>.","ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.","apa":"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 Poincare</i>. Institut Henri Poincaré. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>"},"status":"public","_id":"6240","page":"661-696","publication":"Annales de l'institut Henri Poincare","author":[{"first_name":"Johannes","full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nemish, Yuriy","last_name":"Nemish","first_name":"Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"LaEr"}],"date_created":"2019-04-08T14:05:04Z","date_updated":"2023-10-17T12:20:20Z","publication_identifier":{"issn":["0246-0203"]},"year":"2019","volume":55,"issue":"2","language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"Preprint","publication_status":"published","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"month":"05"}