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  1. Home > Articles & Issues >
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  3. Asynchronous Cellula ...
Conference paper

Asynchronous Cellular Automata and Brownian Motion

Philippe Chassaing (1), Lucas Gerin ORCID (1)
(1) Institut Élie Cartan de Nancy
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Imported on
May 10, 2017
Published on
December 31, 2006
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
Proceedings
DOI
10.46298/dmtcs.3527
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https://about.hal.science/hal-authorisation-v1
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Asynchronous Cellular Automata and Brownian Motion

Philippe Chassaing (1), Lucas Gerin ORCID (1)
(1) Institut Élie Cartan de Nancy
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.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • cellular automata
  • asynchronism
  • random processes
  • coalescent random walks
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