Title: Concentration properties and normal approximation for sample covariance
operators and their spectral projectors

Vladimir Koltchinskii, School of Mathematics, Georgia Tech

Abstract: New moment bounds and concentration inequalities for operator norms
of deviations of sample covariance from the corresponding true covariance
will be discussed. It turns out that the size of such operator norms
could be completely characterized in terms of so called "effective rank"
of the true covariance and its operator norm. The "effective rank" will
be also used to study concentration properties and normal approximation
for bilinear forms of spectral projectors of sample covariance as well
as for squared Hilbert--Schmidt errors of such empirical spectral projectors.
Based on a joint work with Karim Lounici.