---
res:
bibo_abstract:
- "We consider sample covariance matrices of the form X∗X, where X is an M×N matrix
with independent random entries. We prove the isotropic local Marchenko-Pastur
law, i.e. we prove that the resolvent (X∗X−z)−1 converges to a multiple of the
identity in the sense of quadratic forms. More precisely, we establish sharp high-probability
bounds on the quantity ⟨v,(X∗X−z)−1w⟩−⟨v,w⟩m(z), where m is the Stieltjes transform
of the Marchenko-Pastur law and v,w∈CN. We require the logarithms of the dimensions
M and N to be comparable. Our result holds down to scales Iz≥N−1+ε and throughout
the entire spectrum away from 0. We also prove analogous results for generalized
Wigner matrices.\r\n@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Alex
foaf_name: Bloemendal, Alex
foaf_surname: Bloemendal
- 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: Antti
foaf_name: Knowles, Antti
foaf_surname: Knowles
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng
foaf_surname: Yau
- foaf_Person:
foaf_givenName: Jun
foaf_name: Yin, Jun
foaf_surname: Yin
bibo_doi: 10.1214/EJP.v19-3054
bibo_volume: 19
dct_date: 2014^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/10836489
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Isotropic local laws for sample covariance and generalized Wigner matrices@
...