Limit Theorems for Self-Similar Tilings

Alexander I. Bufetov, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

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

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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