Local spectral statistics of Gaussian matrices with correlated entries
Oskari Ajanki, Laszlo Erdos, Torben Kr\"uger
TL;DR
This paper establishes fundamental spectral properties of a class of translation invariant Gaussian matrices with correlated entries, including local laws, universality, and decay of off-diagonal resolvent elements.
Contribution
It provides the first rigorous proof of local spectral laws and universality for correlated Gaussian matrices with translation invariance.
Findings
Proves optimal local spectral law for correlated Gaussian matrices.
Establishes bulk universality in the spectral distribution.
Demonstrates decay properties of off-diagonal resolvent elements.
Abstract
We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.