Self-organisation in Cellular Automata with Coalescent Particles: Qualitative and Quantitative Approaches

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dc.contributor.authorHellouin de Menibus, Benjamin
dc.contributor.authorSablik, Mathieu
dc.date.accessioned2024-05-28T16:32:14Z
dc.date.available2024-05-28T16:32:14Z
dc.date.issued2017-06
dc.descriptionIndexación: Scopus
dc.description.abstractThis article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial configuration at random according to some initial shift-ergodic measure, and use the limit measure to describe the asymptotic behaviour of the automata. We first take a qualitative approach, i.e. we obtain information on the limit measure(s). We prove that only particles moving in one particular direction can persist asymptotically. This provides some previously unknown information on the limit measures of various deterministic and probabilistic cellular automata: 3 and 4-cyclic cellular automata [introduced by Fisch (J Theor Probab 3(2):311–338, 1990; Phys D 45(1–3):19–25, 1990)], one-sided captive cellular automata [introduced by Theyssier (Captive Cellular Automata, 2004)], the majority-traffic cellular automaton, a self stabilisation process towards a discrete line [introduced by Regnault and Rémila (in: Mathematical Foundations of Computer Science 2015—40th International Symposium, MFCS 2015, Milan, Italy, Proceedings, Part I, 2015)]. In a second time we restrict our study to a subclass, the gliders cellular automata. For this class we show quantitative results, consisting in the asymptotic law of some parameters: the entry times [generalising K ůrka et al. (in: Proceedings of AUTOMATA, 2011)], the density of particles and the rate of convergence to the limit measure. © 2017, Springer Science+Business Media New York.
dc.description.urihttps://link.springer.com/article/10.1007/s10955-017-1760-8?utm_source=getftr&utm_medium=getftr&utm_campaign=getftr_pilot
dc.identifier.citationJournal of Statistical Physics Volume 167, Issue 5, Pages 1180 - 12201 June 2017
dc.identifier.doi10.1007/s10955-017-1760-8
dc.identifier.issn0022-4715
dc.identifier.urihttps://repositorio.unab.cl/handle/ria/57180
dc.language.isoen
dc.publisherSpringer New York LLC
dc.rights.licenseCC BY 4.0 DEED Atribución 4.0 Internacional
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/deed.es
dc.subjectBrownian motion
dc.subjectCellular automata
dc.subjectLimit measures
dc.subjectParticles
dc.titleSelf-organisation in Cellular Automata with Coalescent Particles: Qualitative and Quantitative Approaches
dc.typeArtículo
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