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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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.47-58, 2011, DMTCS Proceedings
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Petr Kůrka, Enrico Formenti, Alberto Dennunzio. Asymptotic distribution of entry times in a cellular automaton with annihilating particles. 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.47-58, 2011, DMTCS Proceedings. 〈hal-01196143〉

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