Georgia Institute of Technology College of Sciences

We present a convenient joint generalization of mixing and the local central limit theorem which we call MLLT. We review results on the MLLT for hyperbolic maps and present new results for hyperbolic flows. Then we apply these results to prove global mixing properties of some mechanical systems. These systems include various versions of the Lorentz gas (periodic one; locally perturbed; subject to external fields), the Galton board and pingpong models. Finally, we present applications to random walks in deterministic scenery. This talk is based on joint work with D. Dolgopyat and partially with M. Lenci.