Limit Theorems for Self-Similar Tilings

Alexander I. Bufetov, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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.

Original languageEnglish
Pages (from-to)761-789
Number of pages29
JournalCommunications in Mathematical Physics
Volume319
Issue number3
DOIs
StatePublished - May 2013
Externally publishedYes

Bibliographical note

Funding Information:
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.

Funding Information:
B. S. is supported in part by NSF grant DMS-0968879.

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