Central Limit Theorems For The Double-Struck Capital Z(2)-Periodic Lorentz Gas

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 DOUBLE-STRUCK CAPITAL Z(2)-extensions of dynamical systems (satisfying some nice spectral properties). The motivation of our paper is the DOUBLE-STRUCK CAPITAL Z(2)-periodic Lorentz process for which we establish a functional central limit theorem for Holder continuous observables (in discrete time as well as in continuous time).