Eigenvector decorrelation for random matrices
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.
Fields of Study & Subjects
Random Matrices and Applications
Probability and Risk Models
Matrix Theory and Algorithms
Publication details
- Journal / source
- The Annals of Applied Probability
- Volume
- 36
- Issue
- 4
- Pages
- 3707–3756
- Publication date
- 1 August 2026
- Language
- EN