Anomalous diffusion in deterministic Lorentz gases

The classical Lorentz gas model introduced by Lorentz in 1905, studied further by Sinai in the 1960s, provides a rich source of examples of chaotic dynamical systems with strong stochastic properties (despite being entirely deterministic).  Central limit theorems and convergence to Brownian motion are well understood, both with standard n^{1/2} and nonstandard (n log n)^{1/2} diffusion rates.

In joint work with Paulo Varandas, we discuss examples with diffusion rate n^{1/a}, 1<a<2, and prove convergence to an a-stable Levy process.  This includes to the best of our knowledge the first natural examples where the M_2 Skorokhod topology is the appropriate one.