---
res:
  bibo_abstract:
  - For complex Wigner-type matrices, i.e. Hermitian random matrices with independent,
    not necessarily identically distributed entries above the diagonal, we show that
    at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue
    statistics are universal and form a Pearcey process. Since the density of states
    typically exhibits only square root or cubic root cusp singularities, our work
    complements previous results on the bulk and edge universality and it thus completes
    the resolution of the Wigner–Dyson–Mehta universality conjecture for the last
    remaining universality type in the complex Hermitian class. Our analysis holds
    not only for exact cusps, but approximate cusps as well, where an extended Pearcey
    process emerges. As a main technical ingredient we prove an optimal local law
    at the cusp for both symmetry classes. This result is also the key input in the
    companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where
    the cusp universality for real symmetric Wigner-type matrices is proven. The novel
    cusp fluctuation mechanism is also essential for the recent results on the spectral
    radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random
    matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian
    edge universality (Cipolloni et al. in Edge universality for non-Hermitian random
    matrices, 2019. arXiv:1908.00969).@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: Torben H
      foaf_name: Krüger, Torben H
      foaf_surname: Krüger
      foaf_workInfoHomepage: http://www.librecat.org/personId=3020C786-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4821-3297
  - foaf_Person:
      foaf_givenName: Dominik J
      foaf_name: Schröder, Dominik J
      foaf_surname: Schröder
      foaf_workInfoHomepage: http://www.librecat.org/personId=408ED176-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-2904-1856
  bibo_doi: 10.1007/s00220-019-03657-4
  bibo_volume: 378
  dct_date: 2020^xs_gYear
  dct_identifier:
  - UT:000529483000001
  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 random matrices I: Local law and the complex Hermitian
    case@'
...