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Second-order ergodic theorem for self-similar tiling systems
Published online by Cambridge University Press: 04 July 2013
Abstract
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We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space 
${ \mathbb{R} }^{d} $. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a graph-directed self-similar set associated with the substitution rule.
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