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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2007

Asynchronous Cellular Automata and Brownian Motion

Philippe Chassaing
Lucas Gerin
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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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Dates and versions

hal-00133721 , version 1 (27-02-2007)
hal-00133721 , version 2 (07-06-2007)
hal-00133721 , version 3 (17-08-2015)



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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