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The contact process on a tree: Behavior near the first phase transition

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  • Wu, C. Chris

Abstract

We study the critical behavior of the contact process on a homogeneous tree. It is shown that if the degree of the tree is greater than four, then the survival probability [theta]([lambda]) behaves like ([lambda] - [lambda]c)[beta] with [beta] = 1 when [lambda] is near but above the critical point [lambda]c, and the expected infection time [chi]([lambda]) behaves like ([lambda]c - [lambda])-[gamma] with [gamma] = 1 when [lambda] is near but below [lambda]c. Analogous results for the oriented percolation model are also obtained.

Suggested Citation

  • Wu, C. Chris, 1995. "The contact process on a tree: Behavior near the first phase transition," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 99-112, May.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:99-112
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    References listed on IDEAS

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    1. Griffeath, David, 1981. "The basic contact processes," Stochastic Processes and their Applications, Elsevier, vol. 11(2), pages 151-185, May.
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