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arXiv · 2104.09885

On the Besicovitch-Stability of Noisy Random Tilings

Léopoldine Gayral·Mathieu Sablik
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Abstract

In this paper, we introduce a noisy framework for SFTs, allowing some amount of forbidden patterns to appear. Using the Besicovitch distance, which permits a global comparison of configurations, we then study the closeness of noisy measures to non-noisy ones as the amount of noise goes to 0. Our first main result is the full classification of the (in)stability in the one-dimensional case. Our second main result is a stability property under Bernoulli noise for higher-dimensional periodic SFTs, which we finally extend to an aperiodic example through a variant of the Robinson tiling.

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Léopoldine Gayral, Mathieu Sablik. 2021-04-20. On the Besicovitch-Stability of Noisy Random Tilings. https://doi.org/10.1214/23-ejp917

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