@article{1157,
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.},
author = {Lee, Ji and Schnelli, Kevin},
journal = {Annals of Applied Probability},
number = {6},
pages = {3786 -- 3839},
publisher = {Institute of Mathematical Statistics},
title = {{Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population}},
doi = {10.1214/16-AAP1193},
volume = {26},
year = {2016},
}