---
res:
bibo_abstract:
- We consider N × N Hermitian random matrices with independent identically distributed
entries (Wigner matrices). The matrices are normalized so that the average spacing
between consecutive eigenvalues is of order 1/ N. Under suitable assumptions on
the distribution of the single matrix element, we first prove that, away from
the spectral edges, the empirical density of eigenvalues concentrates around the
Wigner semicircle law on energy scales η ≫ N -1. This result establishes the semicircle
law on the optimal scale and it removes a logarithmic factor from our previous
result [6]. We then show a Wegner estimate, i.e., that the averaged density of
states is bounded. Finally, we prove that the eigenvalues of a Wigner matrix repel
each other, in agreement with the universality conjecture.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Benjamin
foaf_name: Schlein, Benjamin
foaf_surname: Schlein
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
bibo_doi: 10.1093/imrn/rnp136
bibo_issue: '3'
dct_date: 2010^xs_gYear
dct_publisher: Oxford University Press@
dct_title: Wegner estimate and level repulsion for Wigner random matrices@
...