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Article Dans Une Revue Electronic Journal of Probability Année : 2023

On the Besicovitch-Stability of Noisy Random Tilings

Résumé

In this paper, we introduce a framework for studying a subshift of finite type (SFT) with noise, 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 measures on noisy configurations to the non-noisy case 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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Dates et versions

hal-03203745 , version 1 (13-02-2023)

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Gayral Léo, Sablik Mathieu. On the Besicovitch-Stability of Noisy Random Tilings. Electronic Journal of Probability, 2023, 28, ⟨10.1214/23-EJP917⟩. ⟨hal-03203745⟩
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