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Article

Limit Theorems for Self-Similar Tilings

Communications in Mathematical Physics. 2013. Vol. 319. No. 3. P. 761-789.
Bufetov A. I., Solomyak B.

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.