Mixing and its rate in ‘soft’ and ‘hard’ billiards motivated by the Lorentz process

Billiards corresponding to planar periodic Lorentz processes are considered in the usual (hard) sense and in the case when the hard core potential of the scatterers is replaced by some other circularly symmetric potential. A review on certain important aspects of the history of the subject is given and some new results on exponential decay of correlations are formulated. Both the results from the literature and those of our own mentioned are mathematically rigorous, nevertheless, proofs are only briefly sketched. For further details, see the preprint [Correlation decay in certain soft billiards, Commun. Math. Phys., in press].