Universality for diagonal eigenvector overlaps of non-Hermitian random matrices
Abstract
We prove the universality of the joint distribution of an eigenvalue and the corresponding diagonal eigenvector overlap, in the bulk and at the edge, for eigenvalues of complex matrices and real eigenvalues of real matrices. As part of the proof we obtain a bound for the least non-zero singular value of X−z when z is an edge eigenvalue and a bound for the inner product between left and right singular vectors of X−z when |z|=1+O(N−1∕2).
Fields of Study & Subjects
Random Matrices and Applications
Spectral Theory in Mathematical Physics
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–77
- Publication date
- 1 January 2026
- Language
- EN