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

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)651-735
Number of pages85
JournalNew York Journal of Mathematics
Volume16
StatePublished - Dec 1 2010

Keywords

  • Free path length
  • Honeycomb tessellation
  • Limiting distribution
  • Linear flow
  • Planar billiard

ASJC Scopus subject areas

  • Mathematics(all)

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