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

DOI10.1007/S00220-006-0137-7zbMATH Open1143.37002arXivmath/0301270OpenAlexW2123285244MaRDI QIDQ883010

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Publication date: 31 May 2007

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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 $c=2-3ln2+frac27zeta(3)2p{i}^2$ in the asymptotic formula $h(T)=-2lneps+c+o(1)$ of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.

Full work available at URL: https://arxiv.org/abs/math/0301270

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