Abstract
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive ergodic theorems on tilings. The results of this paper can be applied in the study of both random operators and lattice gas models on tilings.
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Received July 19, 2000, and in revised form January 30, 2001. Online publication July 25, 2001.
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Damanik, D., Lenz, D. Linear Repetitivity, I. Uniform Subadditive Ergodic Theorems and Applications. Discrete Comput Geom 26, 411–428 (2001). https://doi.org/10.1007/s00454-001-0033-z
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DOI: https://doi.org/10.1007/s00454-001-0033-z