Bootstrap Percolation, Probabilistic Cellular Automata and Sharpness
Hartarsky, Ivailo (2022), Bootstrap Percolation, Probabilistic Cellular Automata and Sharpness, Journal of Statistical Physics, 187, 3. 10.1007/s10955-022-02922-6
TypeArticle accepté pour publication ou publié
Journal nameJournal of Statistical Physics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, by juggling with these in various directions, we effortlessly obtain a number of new results in these fields. In particular, we prove the sharpness of the phase transition of attractive absorbing probabilistic cellular automata, a class of bootstrap percolation models and kinetically constrained models. We further show how to recover a classical result of Toom on the stability of cellular automata w.r.t. noise and, inversely, how to deduce new results in bootstrap percolation universality from his work.
Subjects / KeywordsProbabilistic cellular automata; Bootstrap percolation; Kinetically constrained models; Sharp phase transition; Stability
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