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arXiv · 1901.00131

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

Mark Demers·Ian Melbourne·Matthew Nicol
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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.

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Mark Demers, Ian Melbourne, Matthew Nicol. 2019-01-01. Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas. https://doi.org/10.1088/1361-6544%2Fab7d22

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