Asymptotic distribution of entry times in a cellular automaton with annihilating particles

Abstract : This work considers a cellular automaton (CA) with two particles: a stationary particle $1$ and left-going one $\overline{1}$. When a $\overline{1}$ encounters a $1$, both particles annihilate. We derive asymptotic distribution of appearence of particles at a given site when the CA is initialized with the Bernoulli measure with the probabilities of both particles equal to $1/2$.
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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, DMTCS Proceedings, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.47-58


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Petr Kůrka, Enrico Formenti, Alberto Dennunzio. Asymptotic distribution of entry times in a cellular automaton with annihilating particles. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2017, DMTCS Proceedings, DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems, pp.47-58. <hal-01196143>

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