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 language | English (US) |
|---|---|
| Pages (from-to) | 651-735 |
| Number of pages | 85 |
| Journal | New York Journal of Mathematics |
| Volume | 16 |
| State | Published - 2010 |
Keywords
- Free path length
- Honeycomb tessellation
- Limiting distribution
- Linear flow
- Planar billiard
ASJC Scopus subject areas
- Mathematics(all)