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Anisotropic contact processes on homogeneous trees

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  • Lalley, Steven P.
  • Sellke, Thomas M.

Abstract

Sufficient conditions are given for the existence of a weak survival phase in a homogeneous but not necessarily isotropic contact process on a homogeneous tree. These require that the contact process be homogeneous, that is, for any two vertices x,y of the tree there is an automorphism mapping x to y leaving the infection rates invariant; and that the contact process be weakly symmetric, that is, for each vertex there should be at least two incident edges with the same infection rate.

Suggested Citation

  • Lalley, Steven P. & Sellke, Thomas M., 2002. "Anisotropic contact processes on homogeneous trees," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 163-183, October.
    • Handle: RePEc:eee:spapps:v:101:y:2002:i:2:p:163-183
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    References listed on IDEAS

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    1. Madras, Neal & Schinazi, Rinaldo, 1992. "Branching random walks on trees," Stochastic Processes and their Applications, Elsevier, vol. 42(2), pages 255-267, September.
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    Cited by:

    1. Durrett, Rick & Jung, Paul, 2007. "Two phase transitions for the contact process on small worlds," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1910-1927, December.

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    1. Durrett, Rick & Jung, Paul, 2007. "Two phase transitions for the contact process on small worlds," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1910-1927, December.

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