Limit theorems for self-similar tilings
Dynamical Systems
2018-02-08 v2
Abstract
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.
Cite
@article{arxiv.1201.6092,
title = {Limit theorems for self-similar tilings},
author = {Alexander I. Bufetov and Boris Solomyak},
journal= {arXiv preprint arXiv:1201.6092},
year = {2018}
}
Comments
36 pages; some corrections and improved exposition, especially in Section 4; references added