[{"OA_place":"repository","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"oa":1,"das_tickbox":"0","supplementarymaterial":"no","article_type":"original","issue":"4","publisher":"Bernoulli Society for Mathematical Statistics and Probability","OA_type":"green","intvolume":"        32","keyword":["correlated random matrix","eigenvalue perturbation theory","Local law","Wigner-type matrix"],"quality_controlled":"1","ec_funded":1,"page":"2999-3023","year":"2026","doi":"10.3150/26-bej1976","citation":{"short":"O. Kolupaiev, Bernoulli 32 (2026) 2999–3023.","ama":"Kolupaiev O. Spectral independence of almost fully correlated random matrices. <i>Bernoulli</i>. 2026;32(4):2999-3023. doi:<a href=\"https://doi.org/10.3150/26-bej1976\">10.3150/26-bej1976</a>","ista":"Kolupaiev O. 2026. Spectral independence of almost fully correlated random matrices. Bernoulli. 32(4), 2999–3023.","ieee":"O. Kolupaiev, “Spectral independence of almost fully correlated random matrices,” <i>Bernoulli</i>, vol. 32, no. 4. Bernoulli Society for Mathematical Statistics and Probability, pp. 2999–3023, 2026.","apa":"Kolupaiev, O. (2026). Spectral independence of almost fully correlated random matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/26-bej1976\">https://doi.org/10.3150/26-bej1976</a>","chicago":"Kolupaiev, Oleksii. “Spectral Independence of Almost Fully Correlated Random Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2026. <a href=\"https://doi.org/10.3150/26-bej1976\">https://doi.org/10.3150/26-bej1976</a>.","mla":"Kolupaiev, Oleksii. “Spectral Independence of Almost Fully Correlated Random Matrices.” <i>Bernoulli</i>, vol. 32, no. 4, Bernoulli Society for Mathematical Statistics and Probability, 2026, pp. 2999–3023, doi:<a href=\"https://doi.org/10.3150/26-bej1976\">10.3150/26-bej1976</a>."},"publication_status":"published","researchdata_availability":"no","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"23112","acknowledgement":"The author is grateful to László Erdős and Giorgio Cipolloni for suggesting the project and fruitful discussions. The author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2503.21472"}],"oa_version":"Preprint","publication":"Bernoulli","author":[{"orcid":"0000-0003-1491-4623","first_name":"Oleksii","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","last_name":"Kolupaiev"}],"scopus_import":"1","external_id":{"arxiv":["2503.21472"]},"arxiv":1,"date_published":"2026-11-01T00:00:00Z","publication_identifier":{"issn":["1350-7265"]},"title":"Spectral independence of almost fully correlated random matrices","type":"journal_article","article_processing_charge":"No","date_created":"2026-10-12T12:04:45Z","volume":32,"fulldoi":"https://doi.org/10.3150/26-bej1976","abstract":[{"lang":"eng","text":"We study the joint spectral properties of two coupled random matrices H(1) and H(2), which are either real symmetric or complex Hermitian. The entries of these matrices exhibit polynomially decaying correlations, both within each matrix and between them. Surprisingly, we find that under extremely weak decorrelation condition, permitting H(1) and H(2) to be almost fully correlated, the fluctuations of their individual eigenvalues in the bulk of the spectrum are still asymptotically independent. Furthermore, we demonstrate that this decorrelation condition is optimal."}],"date_updated":"2026-10-14T07:34:08Z","day":"01","status":"public","department":[{"_id":"LaEr"}],"month":"11","language":[{"iso":"eng"}]}]