2001/01/15 by Roberto Fernández, Roberto Fernandez, Fernandez, Roberto +3 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #60B99 (secondary) #68Q80 #82C20 (primary) 36B15 #Cellular Automata and Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:36B15 #msc:60B99 #msc:68Q80 #msc:82C20
paper · pdf · doi:10.48550/arxiv.math-ph/0101014
29 pages (double space)
arxiv created 2001/01/15 · openalex publication_date 2001/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a class of random cellular automata with multiple invariant measures which are all non-Gibbsian. The automata have configuration space 0,1Zd, with d > 1, and they are noisy versions of automata with the "eroder property". The noise is totally asymmetric in the sense that it allows random flippings of "0" into "1" but not the converse. We prove that all invariant measures assign to the event "a sphere with a large radius L is filled with ones" a probability μL that is too large for the measure to be Gibbsian. For example, for the NEC automaton -ln(μL) ~ L while for any Gibbs measure the corresponding value is ~ L2.