Central limit theorems for the \(\mathbb{Z}^2\)-periodic Lorentz gas (Q2022789)

The authors are interested in stochastic dynamical systems preserving an infinite measure. They prove several central limit theorems for Birkhoff sums of observables of \({\mathbb Z}^2\)-extensions of dynamical systems satisfying suitable spectral properties. For the \({\mathbb Z}^2\)-periodic Lorentz process, they go a step further and establish a functional central limit theorem for Hölder continuous observables in discrete and continuous time.