---
res:
bibo_abstract:
- 'We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs,
that is, graphs on N vertices where every edge is chosen independently and with
probability p = p(N). We rescale the matrix so that its bulk eigenvalues are of
order one. We prove that, as long as pN→∞(with a speed at least logarithmic in
N), the density of eigenvalues of the Erdős-Rényi ensemble is given by the Wigner
semicircle law for spectral windows of length larger than N-1 (up to logarithmic
corrections). As a consequence, all eigenvectors are proved to be completely delocalized
in the sense that the ℓ∞-norms of the ℓ2-normalized eigenvectors are at most of
order N-1/2 with a very high probability. The estimates in this paper will be
used in the companion paper [Spectral statistics of Erdős-Rényi graphs II: Eigenvalue
spacing and the extreme eigenvalues (2011) Preprint] to prove the universality
of eigenvalue distributions both in the bulk and at the spectral edges under the
further restriction that pN »N2/3.@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: Antti
foaf_name: Knowles, Antti
foaf_surname: Knowles
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
- foaf_Person:
foaf_givenName: Jun
foaf_name: Yin, Jun
foaf_surname: Yin
bibo_doi: 10.1214/11-AOP734
bibo_issue: 3 B
bibo_volume: 41
dct_date: 2013^xs_gYear
dct_publisher: Institute of Mathematical Statistics@
dct_title: 'Spectral statistics of Erdős-Rényi graphs I: Local semicircle law@'
...