Abstract. 
Sinai billiard and its extended version to the plane (periodic Lorentz
process) are among the most interesting examples of hyperbolic dynamical
systems. Since the pioneering results of Chernov and Dolgopyat, it became
realistic to prove delicate statistical properties for these models. In the
talk, I will shortly review the development of the theory and focus on some
recent results for periodic Lorentz processes in a strip (i.e. a Sinai
billiard configuration extended in one direction). In particular, I will
discuss the scaling limit of the trajectory of the particle in the presence
of an almost reflecting wall in the tube (joint result with D. Szasz) and
mention some work in progress (with D. Dolgopyat) on the limiting density
profile of non-interacting particles in a long tube with absorbing
boundaries.