The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems


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.


Jens Marklof

School of Mathematics
University of Bristol
Bristol, BS8 1TW
United Kingdom

Andreas Strömbergsson

Department of Mathematics
Box 480
Uppsala University
SE-75106 Uppsala