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- W1797856269 abstract "We consider a class of probabilistic cellular automata undergoing a phase transition with an absorbing-state. Denoting by U(s) the neighbourhood of the site s, the transition probability is T (ηs = 1|ηU(s)) = 0 if ηU(s) = 0 or p otherwise, ∀s ∈ Z. For any U there exists a non-trivial critical probability pc(U) which separates a phase with an absorbing-state from a fluctuating phase. We study how the neighbourhood affects the value of pc(U) and we provide lower bounds for pc(U). Furthermore, using techniques of dynamic renormalization, we prove that the expected convergence time of the processes on a finite space with periodic boundaries grows exponentially (resp. logarithmically) with the system size if p > pc (resp. p < pc). This appears as an open problem in [4, 5, 6]." @default.
- W1797856269 created "2016-06-24" @default.
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- W1797856269 date "2014-03-20" @default.
- W1797856269 modified "2023-09-27" @default.
- W1797856269 title "Critical Probabilities and Convergence Time of Stavskaya's Probabilistic Cellular Automata" @default.
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