---
res:
  bibo_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
    (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven
    only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure
    Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278,
    2018). As our main technical input, we prove an optimal local law at the cusp
    using the <jats:italic>Zigzag strategy</jats:italic>, 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 we also
    provide a significantly simplified alternative proof of the local eigenvalue universality
    in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019)
    and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: László
      foaf_name: Erdös, László
      foaf_surname: Erdös
      foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0001-5366-9603
  - foaf_Person:
      foaf_givenName: Sven Joscha
      foaf_name: Henheik, Sven Joscha
      foaf_surname: Henheik
      foaf_workInfoHomepage: http://www.librecat.org/personId=31d731d7-d235-11ea-ad11-b50331c8d7fb
    orcid: 0000-0003-1106-327X
  - foaf_Person:
      foaf_givenName: Volodymyr
      foaf_name: Riabov, Volodymyr
      foaf_surname: Riabov
      foaf_workInfoHomepage: http://www.librecat.org/personId=1949f904-edfb-11eb-afb5-e2dfddabb93b
  bibo_doi: 10.1007/s00220-025-05417-z
  bibo_issue: '10'
  bibo_volume: 406
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001565019000005
  dct_isPartOf:
  - http://id.crossref.org/issn/0010-3616
  - http://id.crossref.org/issn/1432-0916
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: Cusp universality for correlated random matrices@
...