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Stochastic Analysis of Cellular Automata and the Voter Model

: Mühlenbein, H.; Höns, R.


Bandini, S.; Chopard, B.; Tomassini, M.:
Cellular automata : 5th International Conference on Cellular Automata for Research and Industry, ACRI 2002, Geneva, Switzerland, October 9-11, 2002 ; proceedings
Berlin: Springer, 2002 (Lecture Notes in Computer Science 2493)
ISBN: 3-540-44304-5
ISSN: 0302-9743
International Conference on Cellular Automata for Research and Industry <5, 2002, Genf>
Fraunhofer AIS ( IAIS) ()

We make a stochastic analysis of both deterministic and stochastic cellular automata. The theory uses a mesoscopic view, i.e. it works with probabilities instead of individual configurations used in micro-simulations. We make an exact analysis by using the theory of Markov processes. This can be done for small problems only. For larger problems we approximate the distribution by products of marginal distributions of low order. The approximation use new developments in efficient computation of probabilities based on factorizations of the distribution. We investigate the popular voter model. We show that for one dimension the bifurcation at alpha = 1/3 is an artifact of the mean-field approximation.