Spectral independence of almost fully correlated random matrices
Abstract
We study the joint spectral properties of two coupled random matrices H(1) and H(2), which are either real symmetric or complex Hermitian. The entries of these matrices exhibit polynomially decaying correlations, both within each matrix and between them. Surprisingly, we find that under extremely weak decorrelation condition, permitting H(1) and H(2) to be almost fully correlated, the fluctuations of their individual eigenvalues in the bulk of the spectrum are still asymptotically independent. Furthermore, we demonstrate that this decorrelation condition is optimal.
Fields of Study & Subjects
Random Matrices and Applications
advanced mathematical theories
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 4
- Pages
- 2999–3023
- Publication date
- 31 July 2026
- Language
- EN