Apr 25, 2022
Periodic Lorentz gas with small scatterers
Date: April 25, 2022 |
2:00 pm –
3:00 pm
Speaker:
Peter Balint, Budapest University of Technology and Economics
Location: Mondi Seminar Room 2, Central Building
Language:
English
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, Sz\asz and Varj\u 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.
