Rapid convergence to frequency for Substitution Tilings of the Plane
arXiv:1007.3014 · doi:10.1007/s00220-011-1274-1
Abstract
This paper concerns self-similar tilings in dimension 2. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including most known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.
Minor corrections suggested by the referee. To appear in Communications in Mathematical Physics