On the Besicovitch-Stability of Noisy Random Tilings
Probability
2023-02-14 v2 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2104.09885,
title = {On the Besicovitch-Stability of Noisy Random Tilings},
author = {Léo Gayral and Mathieu Sablik},
journal= {arXiv preprint arXiv:2104.09885},
year = {2023}
}
Comments
The v2 fixes a few typos, as well as a small numerical mistake in the last theorem. 35 pages, 7 figures