Gaussian concentration bounds for probabilistic cellular automata
Probability
2025-07-09 v1
Abstract
We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples.
Keywords
Cite
@article{arxiv.2507.05431,
title = {Gaussian concentration bounds for probabilistic cellular automata},
author = {Jean-René Chazottes and Frank Redig and Edgardo Ugalde},
journal= {arXiv preprint arXiv:2507.05431},
year = {2025}
}