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Conference Papers Year : 2007

Asynchronous Cellular Automata and Brownian Motion

Philippe Chassaing
Lucas Gerin
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Abstract

This paper deals with some very simple interacting particle systems, elementary 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 et 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)

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  • HAL Id : hal-00133721 , version 2

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Philippe Chassaing, Lucas Gerin. Asynchronous Cellular Automata and Brownian Motion. 2007 Conference on Analysis of Algorithms, AofA 07, Jun 2007, Antibes, France. pp 385-402. ⟨hal-00133721v2⟩
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