---
res:
bibo_abstract:
- We consider N×N Hermitian random matrices with i.i.d. entries. The matrix is normalized
so that the average spacing between consecutive eigenvalues is of order 1/N. We
study the connection between eigenvalue statistics on microscopic energy scales
η≪1 and (de)localization properties of the eigenvectors. Under suitable assumptions
on the distribution of the single matrix elements, we first give an upper bound
on the density of states on short energy scales of order η∼log N/N. We then prove
that the density of states concentrates around the Wigner semicircle law on energy
scales η≫N−2/3. We show that most eigenvectors are fully delocalized in the sense
that their ℓp-norms are comparable with N1/p−1/2 for p≥2, and we obtain the weaker
bound N2/3(1/p−1/2) for all eigenvectors whose eigenvalues are separated away
from the spectral edges. We also prove that, with a probability very close to
one, no eigenvector can be localized. Finally, we give an optimal bound on the
second moment of the Green function. @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: 10.1214/08-AOP421
bibo_issue: '3'
bibo_volume: 37
dct_date: 2009^xs_gYear
dct_publisher: Institute of Mathematical Statistics@
dct_title: Semicircle law on short scales and delocalization of eigenvectors for
Wigner random matrices@
...