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Gaussian concentration bounds for probabilistic cellular automata

Journal Article (2025)
Author(s)

Jean René Chazottes (IP Paris, Universidad Autonoma de San Luis Potosi)

F.H.J. Redig (TU Delft - Applied Probability, Universidad Autonoma de San Luis Potosi)

E. Ugalde (Universidad Autonoma de San Luis Potosi)

Research Group
Applied Probability
DOI related publication
https://doi.org/10.1007/s10955-025-03552-4
More Info
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Publication Year
2025
Language
English
Research Group
Applied Probability
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository as part of the Taverne amendment. More information about this copyright law amendment can be found at https://www.openaccess.nl. Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Issue number
12
Volume number
192
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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.

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