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Comm. Math. Phys., 2013, Volume 319, Issue 3, Pages 761–769 (Mi cmph6)  

Limit theorems for self-similar tilings

A. I. Bufetovabcde, B. Solomyakf

a Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia
b Natl Res Univ, Higher Sch Econ, Moscow, Russia
c Rice Univ, Dept Math, Houston, TX 77005
d VA Steklov Math Inst, Moscow 117333, Russia
e Aix Marseille Univ, Lab Anal, CNRS, Marseille, France
f Univ Washington, Dept Math, Seattle, WA 98195 USA

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.

Funding Agency Grant Number
Dynasty Foundation
Alfred P. Sloan Foundation
Simons Foundation
Ministry of Education and Science of the Russian Federation MK 6734.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 10-01-93115
11-01-00654
National Science Foundation DMS-0968879
A. B. is an Alfred P. Sloan Fellow, a Dynasty Foundation Fellow, and an IUM-Simons Fellow. He is supported in part by the Grant MK 6734.2012.1 of the President of the Russian Federation, by the Programme on Dynamical Systems and Mathematical Control Theory of the Presidium of the Russian Academy of Sciences, by RFBR-CNRS grant 10-01-93115 and by the RFBR grant 11-01-00654. B. S. is supported in part by NSF grant DMS-0968879.


DOI: https://doi.org/10.1007/s00220-012-1624-7


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Received: 03.02.2012
Accepted:26.03.2012
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