article published yes 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 GradSch department Random matrices beyond Wigner-Dyson-Mehta project We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices 𝑊 +𝐷1, 𝑊 +𝐷2 and show that their bulk eigenvectors become asymptotically orthogonal as soon as Tr⁡(𝐷1−𝐷2)2 ≫1, or their respective energies are separated on a scale much bigger than the local eigenvalue spacing. Furthermore, we show that quadratic forms of eigenvectors of 𝑊 +𝐷1, 𝑊 +𝐷2 with any deterministic matrix 𝐴 ∈𝐂𝑁×𝑁 in a specific subspace of codimension one are of size 𝑁−1/2. This proves a generalization of the eigenstate thermalization hypothesis to eigenvectors belonging to two different spectral families. Institute of Mathematical Statistics2026 eng characteristic flowDavis–Kahan theoremEigenstate thermalizationEigenvector perturbation theoryLocal lawzigzag strategy 1050-5164 2410.1071810.1214/26-AAP2318 3643707-3756 https://research-explorer.ista.ac.at/record/19546 Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for random matrices. <i>Annals of Applied Probability</i>. 2026;36(4):3707-3756. doi:<a href="https://doi.org/10.1214/26-AAP2318">10.1214/26-AAP2318</a> Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2026. Eigenvector decorrelation for random matrices. Annals of Applied Probability. 36(4), 3707–3756. G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Annals of Applied Probability 36 (2026) 3707–3756. Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Eigenvector Decorrelation for Random Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2026. <a href="https://doi.org/10.1214/26-AAP2318">https://doi.org/10.1214/26-AAP2318</a>. Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2026). Eigenvector decorrelation for random matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/26-AAP2318">https://doi.org/10.1214/26-AAP2318</a> G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation for random matrices,” <i>Annals of Applied Probability</i>, vol. 36, no. 4. Institute of Mathematical Statistics, pp. 3707–3756, 2026. Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.” <i>Annals of Applied Probability</i>, vol. 36, no. 4, Institute of Mathematical Statistics, 2026, pp. 3707–56, doi:<a href="https://doi.org/10.1214/26-AAP2318">10.1214/26-AAP2318</a>. 229232026-09-13T22:01:54Z2026-09-16T10:00:54Z