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Peierls bounds from Toom contours

Swart, Jan M.; Szabo, Reka; Toninelli, Cristina (2022), Peierls bounds from Toom contours. https://basepub.dauphine.psl.eu/handle/123456789/23288

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
61
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Author(s)
Swart, Jan M.
Szabo, Reka
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Toninelli, Cristina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We review and extend Toom's classical result about stability of trajectories of cellular automata, with the aim of deriving explicit bounds for monotone Markov processes, both in discrete and continuous time. This leads, among other things, to rigorous bounds for a two-dimensional interacting particle system with cooperative branching and deaths. Our results can be applied to derive bounds for other monotone systems as well.
Subjects / Keywords
Random Cellular Automata; Monotone Interacting Particle Systems; Toom’s theorem