Conservation Laws and Invariant Measures in Surjective Cellular Automata

Jarkko Kari 1 Siamak Taati 2
1 FUNDIM - Departement of Mathematics, University of Turku
2 University of Groningen - Department of Mathematics
Abstract : We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.
Keywords : surjective cellular automata conservation laws invariant measures statistical equilibrium
Type de document :
Communication dans un congrès
Fatès, Nazim and Goles, Eric and Maass, Alejandro and Rapaport, Iván. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.113-122, 2011, DMTCS Proceedings
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Dernière modification le : mercredi 29 août 2018 - 11:02:02
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Jarkko Kari, Siamak Taati. Conservation Laws and Invariant Measures in Surjective Cellular Automata. Fatès, Nazim and Goles, Eric and Maass, Alejandro and Rapaport, Iván. 17th International Workshop on Celular Automata and Discrete Complex Systems, 2011, Santiago, Chile. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.113-122, 2011, DMTCS Proceedings. 〈hal-01196135〉

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