New York Journal of Mathematics
Volume 16 (2010) 651-735


Florin P. Boca

Distribution of the linear flow length in a honeycomb in the small-scatterer limit

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Published: December 11, 2010
Keywords: Honeycomb tessellation, linear flow, planar billiard, free path length, limiting distribution
Subject: 37D50 (11B57, 11P21, 82C40)

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.

Author information

Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USA

Member of the Institute of Mathematics "Simion Stoilow" of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania