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Distribution of the linear flow length in a honeycomb in the small-scatterer limit. (English) Zbl 1221.37075

Summary: We study the statistics of the linear flow in a punctured honeycomb lattice, or equivalently the free motion of a particle on a regular hexagonal billiard table, with holes of equal size at the corners, obeying the customary reflection rules. In the small-scatterer limit we prove the existence of the limiting distribution of the free path length with randomly chosen origin of the trajectory, and explicitly compute it.

MSC:

37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
11P21 Lattice points in specified regions
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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