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On Critical Values for Some Random Processes with Local Interaction in R2

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In and Out of Equilibrium

Part of the book series: Progress in Probability ((PRPR,volume 51))

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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Reference

  1. 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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  2. A. L. Toom, Stable and attractive trajectories in multicomponent systems. In Multicomponent Random Systems(R. Dobrushin and Ya. Sinai, eds.).Advances in Probability and Related Topics, vol. 6, Dekker, 1980, pp. 549–576

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  3. A. L. Toom, Monotonic evolutions in real spaces. In InLocally Interacting Systems and Their Application in Biology(R.Dobrushin, V.Kryukov, and A.Toom, eds.). Lecture Notes in Mathematics, vol. 653, Springer, 1978, pp. 1–14.

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Author information

Authors and Affiliations

  1. Department of Statistics, Federal University of Pernambuco Recife/PE, 50740-540, Brazil

    André Toom

Authors
  1. André Toom
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Editor information

Editors and Affiliations

  1. IMPA-Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110 Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil

    Vladas Sidoravicius

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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

  • eBook Packages: Springer Book Archive

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