---
res:
bibo_abstract:
- We consider the ensemble of adjacency matrices of Erdős-Rényi random graphs, i.e.
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.
Under the assumption pN≫N2/3 , we prove the universality of eigenvalue distributions
both in the bulk and at the edge of the spectrum. More precisely, we prove (1)
that the eigenvalue spacing of the Erdős-Rényi graph in the bulk of the spectrum
has the same distribution as that of the Gaussian orthogonal ensemble; and (2)
that the second largest eigenvalue of the Erdős-Rényi graph has the same distribution
as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application
of our method, we prove the bulk universality of generalized Wigner matrices under
the assumption that the matrix entries have at least 4 + ε moments.@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: 10.1007/s00220-012-1527-7
bibo_issue: '3'
bibo_volume: 314
dct_date: 2012^xs_gYear
dct_publisher: Springer@
dct_title: 'Spectral statistics of Erdős-Rényi graphs II: Eigenvalue spacing and
the extreme eigenvalues@'
...