Abstract
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).
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Acknowledgments
This research has been done mostly in the Mathematical Departments of Brest and Orsay Universities, and also at the Institut Henri Poincaré that we thank for their hospitalities. FP is grateful to the Institut Universitaire de France (IUF) for its important support.
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Pène, F., Thomine, D. Central limit theorems for the ℤ2-periodic Lorentz gas. Isr. J. Math. 241, 539–582 (2021). https://doi.org/10.1007/s11856-021-2106-4
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DOI: https://doi.org/10.1007/s11856-021-2106-4