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On the Connection Between Oriented Percolation and Contact Process

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Abstract

We study the contact process in \({\mathbb{Z}}\) d and a family of two-parametric oriented percolation models in \({\mathbb{Z}}\) d×\({\mathbb{Z}}\) +. It is proved that the derivative at the endpoint of the critical curve for percolation exists and its absolute value coincides with the critical rate for the corresponding contact process.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, South Road, Durham, DH1 3LE, United Kingdom

    M. V. Menshikov

  2. Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, mailbox 66.281, CEP 05315–970, São Paulo, SP, Brazil

    S. Yu. Popov & V. V. Sisko

  3. Institute for Problems of Information Transmission of Russian Academy of Sciences, B. Karetny 19, 101447, Moscow, Russia

    S. Yu. Popov

Authors
  1. M. V. Menshikov
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  2. S. Yu. Popov
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  3. V. V. Sisko
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Menshikov, M.V., Popov, S.Y. & Sisko, V.V. On the Connection Between Oriented Percolation and Contact Process. Journal of Theoretical Probability 15, 207–221 (2002). https://doi.org/10.1023/A:1013847619585

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  • DOI: https://doi.org/10.1023/A:1013847619585

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