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

Nonlinearity 33 (2020) 4095-4113.

Mark Demers, Ian Melbourne and Matthew Nicol

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 Hölder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles.

pdf file

Typos, etc: None known in our pdf file, but certainly some typos were introduced in the published version as part of the added value from the publishing house. So on p. 4103 just before Lemma 3.2, h_n(x) has become h_n(X). In the proof of Lemma 3.2, int_Y has become int Y.