Asynchronous Cellular Automata and Brownian Motion

Philippe Chassaing (1) , Lucas Gerin (1)

1 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: cellular automata; asynchronism; random processes; coalescent random walks

Domaines: Probabilités [math.PR]

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⟩