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|
|Pages (from-to)||1949 - 2033|
|Number of pages||85|
|Journal||Annals of Mathematics|
|Publication status||Published - Nov 2010|