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arXiv · 1909.05514

Central limit theorems for the $\mathbb{Z}^2$-periodic Lorentz gas

Françoise Pène·Damien Thomine
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Abstract

This paper is devoted to the study of the stochastic properties of dynamical systems preserving an infinite measure. More precisely we prove central limit theorems for Birkhoff sums of observables of $\mathbb{Z}^2$-extensions of dynamical systems (satisfying some nice spectral properties). The motivation of our paper is the $\mathbb{Z}^2$-periodic Lorentz process for which we establish a functional central limit theorem for H\"older continuous observables (in discrete time as well as in continuous time).

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Françoise Pène, Damien Thomine. 2019-09-12. Central limit theorems for the $\mathbb{Z}^2$-periodic Lorentz gas. https://arxiv.org/abs/1909.05514

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