Entry times in automata with simple defect dynamics

Benjamin Hellouin De Menibus
(Université d'Aix-Marseille, France)
Mathieu Sablik
(Université d'Aix-Marseille, France)

In this paper, we consider a simple cellular automaton with two particles of different speeds that annihilate on contact. Following a previous work by K\r urka et al., we study the asymptotic distribution, starting from a random configuration, of the waiting time before a particle crosses the central column after time n. Drawing a parallel between the behaviour of this automata on a random initial configuration and a certain random walk, we approximate this walk using a Brownian motion, and we obtain explicit results for a wide class of initial measures and other automata with similar dynamics.

In Enrico Formenti: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), La Marana, Corsica, September 19-21, 2012, Electronic Proceedings in Theoretical Computer Science 90, pp. 97–109.
Published: 13th August 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.90.8 bibtex PDF
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