Statistical properties of the system of two falling balls

We consider the motion of two point masses along a vertical half-line that are subject to constant gravitational force and collide elastically with each other and the floor. This model was introduced by Wojtkowski who established hyperbolicity and ergodicity in case the lower ball is heavier. Here, we investigate the dynamics in discrete time and prove that, for an open set of the external parameter (the relative mass of the lower ball), the system mixes polynomially—modulo logarithmic factors, correlations decay as O(1/n2)—and satisfies the Central Limit Theorem.