2026/02/14 by Emilio N. M. Cirillo, Joram L. Vliem, Dirk Schuricht +1 · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #math.PR #msc:37B15 #msc:60K35 #nlin.CG
paper · pdf · doi:10.1103/qksd-scrd
published as Phys. Rev. E 114, 014154 (2026) · 8 figures
arxiv created 2026/02/14 · arxiv published 2026/02/14 · arxiv updated 2026/08/07
We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that, for any finite periodic lattice and for mixing parameter λ=1/2, the system almost surely reaches the absorbing all-zero configuration in finitely many steps. In addition, Monte Carlo simulations indicate as well the presence of a zero-density stationary state in a finite interval around λ=1/2. Despite this absorbing behavior, both mean-field and block approximation schemes predict a stationary state with non-zero density. This failure, traced to the additive and mirror symmetries of the deterministic components, highlights a fundamental limitation of finite-block approximation in capturing the global dynamics of probabilistic cellular automata.