The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit |
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| Authors: | Florin P. Boca Alexandru Zaharescu |
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| Affiliation: | (1) Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA;(2) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania |
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| Abstract: | We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term  in the asymptotic formula  of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp |
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