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Asynchronous Cellular Automata and Brownian Motion

Abstract : This paper deals with some very simple interacting particle systems, \emphelementary cellular automata, in the fully asynchronous dynamics: at each time step, a cell is randomly picked, and updated. When the initial configuration is simple, we describe the asymptotic behavior of the random walks performed by the borders of the black/white regions. Following a classification introduced by Fatès \emphet al., we show that four kinds of asymptotic behavior arise, two of them being related to Brownian motion.
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https://hal.inria.fr/hal-00133721
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Submitted on : Monday, August 17, 2015 - 4:59:06 PM
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Philippe Chassaing, Lucas Gerin. Asynchronous Cellular Automata and Brownian Motion. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.423-442, ⟨10.46298/dmtcs.3527⟩. ⟨hal-00133721v3⟩

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