Periodic Lorentz gas with small scatterers.

We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time tends to infinity, the scatterer size may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Central Limit Theorem as well as a Local Limit Theorem for the displacement function. To the best of our knowledge, these are the first results on an intermediate case between the two well-studied regimes with superdiffusive scaling (i) for fixed infinite horizon configurations-letting first and then -studied e.

Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension.

We describe a fast and accurate method to compute the pressure and equilibrium states for maps of the interval T:[0,1]-->[0,1] with respect to potentials phi:[0,1]-->R. An approximate Ruelle-Perron-Frobenius operator is constructed and the pressure read off as the logarithm of the leading eigenvalue of this operator. By setting phi identical with 0, we recover the topological entropy.