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The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems. (English) Zbl 1211.82011

The distribution of the free path length in the periodic Lorentz gas was already investigated by G. Pólya, who rephrased the problem in terms of the visibility in a (periodic) forest [Arch. d. Math. u. Phys. (3) 27, 135–142 (1918; JFM 46.0284.01)]. In this paper the authors establish a Markov property, and provide explicit formulas and asymptotic estimates for the limiting distribution.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
11P21 Lattice points in specified regions
37A60 Dynamical aspects of statistical mechanics
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C40 Kinetic theory of gases in time-dependent statistical mechanics

Citations:

JFM 46.0284.01
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References:

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