Limit theorems for self-similar tilings

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.

36 pages; some corrections and improved exposition, especially in Section 4; references added

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Cited by in corpus (10)

• Singular substitutions of constant length
• Self affine Delone sets and deviation phenomena
• Universal hitting time statistics for integrable flows
• Random Substitution Tilings and Deviation Phenomena
• Spectral cocycle for substitution tilings
• Rotation numbers and rotation classes on one-dimensional tiling spaces
• Graph towers, laminations and their invariant measures
• Tilings and traces
• Statistical properties of Lorentz gases on aperiodic tilings, Part 1
• Balancedness and coboundaries in symbolic systems