## 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 |
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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 |