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

J Marklof, A Strombergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

48 Citations (Scopus)

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 contributionThe distribution of free path lengths in the periodic Lorentz gas and elated lattice point problems
Original languageEnglish
Pages (from-to)1949 - 2033
Number of pages85
JournalAnnals of Mathematics
Volume172
Issue number3
DOIs
Publication statusPublished - Nov 2010

Bibliographical note

Publisher: Princeton University

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