Eigenvector decorrelation for random matrices Cipolloni, Giorgio ; https://orcid.org/0000-0002-4901-7992 Erdös, László ; https://orcid.org/0000-0001-5366-9603 Henheik, Sven Joscha ; https://orcid.org/0000-0003-1106-327X Kolupaiev, Oleksii ; https://orcid.org/0000-0003-1491-4623 characteristic flow Davis–Kahan theorem Eigenstate thermalization Eigenvector perturbation theory Local law zigzag strategy 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 Statistics 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22923 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1214/26-AAP2318 info:eu-repo/semantics/altIdentifier/issn/1050-5164 info:eu-repo/semantics/altIdentifier/arxiv/2410.10718 info:eu-repo/semantics/openAccess