The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit

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dc.creatorBoca, Florin P.
dc.creatorZaharescu, Alexandru
dc.date2003-01-23
dc.date2006-07-13
dc.date.accessioned2026-07-07T06:35:34Z
dc.date.available2026-07-07T06:35:34Z
dc.descriptionWe 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 $c=2-3\ln 2+\frac{27ζ(3)}{2π^2}$ in the asymptotic formula $h(T)=-2\ln \eps+c+o(1)$ of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.
dc.identifierhttps://arxiv.org/abs/math/0301270
dc.identifierhttp://arxiv.org/abs/math/0301270
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99833
dc.subjectNumber Theory
dc.subjectMathematical Physics
dc.subjectDynamical Systems
dc.subjectPrimary: 11K60 Secondary: 11P21; 11J83; 37A60;37A60; 37D50; 82C05; 82C40
dc.titleThe distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit
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