article epub_ahead yes Zhigang Bao author 442E6A6C-F248-11E8-B48F-1D18A9856A870000-0003-3036-1475 Giorgio Cipolloni author 42198EFA-F248-11E8-B48F-1D18A9856A870000-0002-4901-7992 László Erdös author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603 Sven Joscha Henheik author 31d731d7-d235-11ea-ad11-b50331c8d7fb0000-0003-1106-327X Oleksii Kolupaiev author 149b70d4-896a-11ed-bdf8-8c63fd44ca610000-0003-1491-4623 LaEr department Random matrices beyond Wigner-Dyson-Mehta project We consider the Wigner minor process, i.e. the eigenvalues of an N\times N Wigner matrix H^{(N)} together with the eigenvalues of all its n\times n minors, H^{(n)}, n\le N. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality. Springer Nature2025 eng 0178-8051 1432-2064 2503.06549 00157464090000110.1007/s00440-025-01422-4 Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields. Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s00440-025-01422-4">10.1007/s00440-025-01422-4</a>. Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025). Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-025-01422-4">https://doi.org/10.1007/s00440-025-01422-4</a> Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href="https://doi.org/10.1007/s00440-025-01422-4">10.1007/s00440-025-01422-4</a> Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href="https://doi.org/10.1007/s00440-025-01422-4">https://doi.org/10.1007/s00440-025-01422-4</a>. 204782025-10-16T13:10:26Z2026-06-18T18:23:40Z