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In this paper, we show how the Gordin martingale approximation method fitsinto the anisotropic Banach space framework. In particular, for the time-onemap of a finite horizon planar periodic Lorentz gas, we prove that Holderobservables satisfy statistical limit laws such as the central limit theoremand associated invariance principles.

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