Abstract
The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad limit, where the radius of each scatterer tends to zero, and prove the existence of a limiting distribution for the free path length. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed position.
| Translated title of the contribution | The distribution of free path lengths in the periodic Lorentz gas and elated lattice point problems |
|---|---|
| Original language | English |
| Pages (from-to) | 1949 - 2033 |
| Number of pages | 85 |
| Journal | Annals of Mathematics |
| Volume | 172 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Nov 2010 |