Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas

Abstract: In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles.