10.46298/dmtcs.2968
https://dmtcs.episciences.org/2968
Kari, Jarkko
Jarkko
Kari
Taati, Siamak
Siamak
Taati
0000-0002-6503-2754
Academy of Finland
131558
Cellular automata and discrete dynamical systems
Conservation Laws and Invariant Measures in Surjective Cellular Automata
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.
episciences.org
surjective cellular automata
conservation laws
invariant measures
statistical equilibrium
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]
[NLIN.NLIN-CG] Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
2023-03-28
2011-01-01
2011-01-01
en
journal article
https://hal.science/hal-01196135v1
1365-8050
https://dmtcs.episciences.org/2968/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
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