---
res:
bibo_abstract:
- We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where
the sample X is an M ×N random matrix whose entries are real independent random
variables with variance 1/N and whereσ is an M × M positive-definite deterministic
matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue
of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class
of populations σ in the sub-critical regime, we show that the distribution of
the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution
under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians
or (2) that σ is diagonal and that the entries of X have a sub-exponential decay.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Ji
foaf_name: Lee, Ji
foaf_surname: Lee
- foaf_Person:
foaf_givenName: Kevin
foaf_name: Schnelli, Kevin
foaf_surname: Schnelli
foaf_workInfoHomepage: http://www.librecat.org/personId=434AD0AE-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-0954-3231
bibo_doi: 10.1214/16-AAP1193
bibo_issue: '6'
bibo_volume: 26
dct_date: 2016^xs_gYear
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Tracy-widom distribution for the largest eigenvalue of real sample covariance
matrices with general population@
...