Periodic Lorentz gas with small scatterers

Speaker. Peter Balint
Date. 25.04.22 at 2:00 pm

Abstract. The planar periodic Lorentz gas describes the motion of a billiard particle in a periodic arrangement of convex scatterers. The case of infinite horizon — when the flight time between consecutive collisions is unbounded — is a popular model of anomalous diffusion. For fixed scatterer size, Szász and Varjú proved a limit theorem for the displacement of the particle with a non-standard \sqrt{n \log n} scaling. In my talk I would like to describe the asymptotics of this limit law in a setting when as time n tends to infinity, the scatterer size may also tend to zero simultaneously at a sufficiently slow pace. This is joint work with Henk Bruin and Dalia Terhesiu.