@article{22923,
  abstract     = {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.},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  issn         = {1050-5164},
  journal      = {Annals of Applied Probability},
  keywords     = {characteristic flow, Davis–Kahan theorem, Eigenstate thermalization, Eigenvector perturbation theory, Local law, zigzag strategy},
  number       = {4},
  pages        = {3707--3756},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Eigenvector decorrelation for random matrices}},
  doi          = {10.1214/26-AAP2318},
  volume       = {36},
  year         = {2026},
}