@unpublished{19547,
  abstract     = {For correlated real symmetric or complex Hermitian random matrices, we prove
that the local eigenvalue statistics at any cusp singularity are universal.
Since the density of states typically exhibits only square root edge or cubic
root cusp singularities, our result completes the proof of the
Wigner-Dyson-Mehta universality conjecture in all spectral regimes for a very
general class of random matrices. Previously only the bulk and the edge
universality were established in this generality [arXiv:1804.07744], while cusp
universality was proven only for Wigner-type matrices with independent entries
[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an
optimal local law at the cusp using the Zigzag strategy, a recursive tandem of
the characteristic flow method and a Green function comparison argument.
Moreover, our proof of the optimal local law holds uniformly in the spectrum,
thus also re-establishing universality of the local eigenvalue statistics in
the previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]
regimes.},
  author       = {Erdös, László and Henheik, Sven Joscha and Riabov, Volodymyr},
  booktitle    = {arXiv},
  title        = {{Cusp universality for correlated random matrices}},
  doi          = {10.48550/arXiv.2410.06813},
  year         = {2024},
}