Abstract
We complete the proof of a necessary and sufficient condition for existence of non-trivial critical values for some classes of random processes with local interaction, where the space is a real plane. Our operators are superpositions of a deterministic operator and a one-sided random noise, where the noise is standard and the geometric properties of the deterministic operator are crucial.
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A. Toom, N. Vasilyev, O. Stayskaya, L. Mityushin, G. Kurdyumov, and S. Pirogov, Discrete local Markov systems. In Stochastic Cellular Systems: Ergodicity,Memory,Morphogenesis(R. Dobrushin, V. Kryukov, and A. Toom, eds.).Nonlinear Science: Theory and Applications, Manchester University Press, 1990, pp. 1–182
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© 2002 Springer Science+Business Media New York
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Toom, A. (2002). On Critical Values for Some Random Processes with Local Interaction in R2 . In: Sidoravicius, V. (eds) In and Out of Equilibrium. Progress in Probability, vol 51. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0063-5_14
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DOI: https://doi.org/10.1007/978-1-4612-0063-5_14
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6595-5
Online ISBN: 978-1-4612-0063-5
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