Geodesic
The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
Jens Marklof1 ; Andreas Strömbergsson 2
1 School of Mathematics<br/>University of Bristol<br/>Bristol, BS8 1TW<br/>United Kingdom
2 Department of Mathematics<br/>Box 480<br/>Uppsala University<br/>SE-75106 Uppsala<br/>Sweden
Annals of mathematics, Tome 172 (2010) no. 3, pp. 1949-2033

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

DOI : 10.4007/annals.2010.172.1949

Jens Marklof 1 ; Andreas Strömbergsson  2

1 School of Mathematics<br/>University of Bristol<br/>Bristol, BS8 1TW<br/>United Kingdom
2 Department of Mathematics<br/>Box 480<br/>Uppsala University<br/>SE-75106 Uppsala<br/>Sweden 
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Jens Marklof; Andreas Strömbergsson . The distribution of free path lengths  in the periodic Lorentz gas and  related lattice point problems. Annals of mathematics, Tome 172 (2010) no. 3, pp. 1949-2033. doi: 10.4007/annals.2010.172.1949

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