This paper is devoted to the stochastic properties of dynamical systems preserving an infinite measure. More precisely we prove central limit theorems for Birkhoff sums of observables of ℤ²-extensions of dynamical systems (satisfying some nice spectral properties). The motivation of our paper is the ℤ²-periodic Lorentz process for which we establish a functional central limit theorem for Hölder continuous observables (in discrete time as well as in continuous time).

中文翻译：

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ℤ2-周期洛伦兹气体的中心极限定理

本文致力于保留无限度量的动力学系统的随机特性。更确切地说，我们证明了ℤ的观测值的总和伯克霍夫中心极限定理^2个-Extensions动力系统（满足一些不错的光谱特性）。我们的纸的动机是ℤ ²为周期洛伦兹过程为此我们建立赫尔德连续可观测量的功能性中心极限定理（在离散时间，以及在连续的时间）。