Geodesic
Asynchronous Cellular Automata and Brownian Motion
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007).

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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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     author = {Chassaing, Philippe and Gerin, Lucas},
     title = {Asynchronous {Cellular} {Automata} and {Brownian} {Motion}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     year = {2007},
     doi = {10.46298/dmtcs.3527},
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Chassaing, Philippe; Gerin, Lucas. Asynchronous Cellular Automata and Brownian Motion. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi : 10.46298/dmtcs.3527. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3527/

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