---
res:
  bibo_abstract:
  - Let U and V be two independent N by N random matrices that are distributed according
    to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The
    single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the
    empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the
    limit of large N, to a deterministic measure which is supported on a single ring
    centered at the origin in ℂ. Within the bulk regime, that is, in the interior
    of the single ring, we establish the convergence of the empirical eigenvalue distribution
    on the optimal local scale of order N−1/2+ε and establish the optimal convergence
    rate. The same results hold true when U and V are Haar distributed on O(N).@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Zhigang
      foaf_name: Bao, Zhigang
      foaf_surname: Bao
      foaf_workInfoHomepage: http://www.librecat.org/personId=442E6A6C-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0003-3036-1475
  - 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: Kevin
      foaf_name: Schnelli, Kevin
      foaf_surname: Schnelli
      foaf_workInfoHomepage: http://www.librecat.org/personId=434AD0AE-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0003-0954-3231
  bibo_doi: 10.1214/18-AOP1284
  bibo_issue: '3'
  bibo_volume: 47
  dct_date: 2019^xs_gYear
  dct_identifier:
  - UT:000466616100003
  dct_isPartOf:
  - http://id.crossref.org/issn/0091-1798
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_title: Local single ring theorem on optimal scale@
...