Journal
ANNALS OF MATHEMATICS
Volume 172, Issue 3, Pages 1949-2033Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2010.172.1949
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Funding
- EPSRC
- Philip Leverhulme Prize
- Knut and Alice Wallenberg Foundation
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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.
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