We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Mesoscopic central limit theorem for non-Hermitian random matrices.
- Authors
Cipolloni, Giorgio; Erdős, László; Schröder, Dominik
- Abstract
We prove that the mesoscopic linear statistics ∑ i f (n a (σ i - z 0)) of the eigenvalues { σ i } i of large n × n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H 0 2 -functions f around any point z 0 in the bulk of the spectrum on any mesoscopic scale 0 < a < 1 / 2 . This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a = 0 , to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z 1 , z 2 with an improved error term in the entire mesoscopic regime | z 1 - z 2 | ≫ n - 1 / 2 . The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator.
- Subjects
CENTRAL limit theorem; RANDOM matrices; COMPLEX matrices; MATHEMATICS; NONEXPANSIVE mappings
- Publication
Probability Theory & Related Fields, 2024, Vol 188, Issue 3/4, p1131
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-023-01229-1