Relative perturbation bounds with applications to empirical covariance operators

The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions eigenvalues and spectral projectors, leading concentration inequalities limit theorems. One the key ingredients a specific separation measure population eigenvalues, which we call rank, giving rise sharp invariance principle in terms theorems, inconsistency results. framework very general, requiring only p>4 moments allows huge variety dependence structures.