A universality result for the smallest eigenvalues of certain sample covariance matrices
Mathematical Physics
2011-01-25 v4 math.MP
Probability
Abstract
After proper rescaling and under some technical assumptions, the smallest eigenvalue of a sample covariance matrix with aspect ratio bounded away from 1 converges to the Tracy--Widom distribution. This complements the results on the largest eigenvalue, due to Soshnikov and Peche.
Keywords
Cite
@article{arxiv.0812.1961,
title = {A universality result for the smallest eigenvalues of certain sample covariance matrices},
author = {Ohad N. Feldheim and Sasha Sodin},
journal= {arXiv preprint arXiv:0812.1961},
year = {2011}
}
Comments
53 pages, 7 figures. To appear in Geom. Funct. Anal