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<p>We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired by the work of Bufetov and Solomyak [<CitationRef CitationID="CR8">8</CitationRef>], where they established a log-Hölder modulus of continuity of one-dimensional self-similar tiling systems. We generalize this result to higher dimensions in the more general setting of self-affine tilings systems. Further analysis leads to uniform estimates in the whole space of spectral parameters, allowing to deduce logarithmic rates of weak mixing.</p>

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Quantitative weak mixing of self-affine tilings

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  • 发表日期：

    2026年2月2日

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  • Juan Marshall-Maldonado

摘要

We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired by the work of Bufetov and Solomyak [8], where they established a log-Hölder modulus of continuity of one-dimensional self-similar tiling systems. We generalize this result to higher dimensions in the more general setting of self-affine tilings systems. Further analysis leads to uniform estimates in the whole space of spectral parameters, allowing to deduce logarithmic rates of weak mixing.