Quantitative weak mixing of self-affine tilings
Dynamical Systems
2025-01-07 v2
Abstract
We study the regularity of spectral measures of dynamical systems arising from a translation action on tilings of substitutive nature. The results are inspired in the work of Bufetov and Solomyak, where they established a log-H\"older 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.
Cite
@article{arxiv.2408.13228,
title = {Quantitative weak mixing of self-affine tilings},
author = {Juan Marshall-Maldonado},
journal= {arXiv preprint arXiv:2408.13228},
year = {2025}
}