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The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2010 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 172, no 3, 1949-2033 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 172, no 3, 1949-2033 p.
Keyword [en]
SURE INVARIANCE-PRINCIPLE, STATISTICAL PROPERTIES, INFINITE-HORIZON, LIMIT, EQUIDISTRIBUTION, RECURRENCE, SYSTEMS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-26621DOI: 10.4007/annals.2010.172.1949ISI: 000282652000012Scopus ID: 2-s2.0-77957898198OAI: oai:DiVA.org:kth-26621DiVA: diva2:374771
Note
QC 20101206Available from: 2010-12-06 Created: 2010-11-26 Last updated: 2017-12-11Bibliographically approved

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