Almost sure invariance principle by spectral methods

2010. szeptember 23., csütörtök, 17:15

The (vector-valued) almost sure invariance principle is a strong reinforcement of the central limit theorem. I will explain how to prove it for Birkhoff sums of dynamical systems, solely under a spectral assumption on perturbed transfer operators. Contrary to many classical situations, this assumption is not formulated in terms of the behavior of a perturbed eigenvalue (I do not even require the existence of such an eigenvalue).