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

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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 θ(λ) behaves like (λ - λc)β with β = 1 when λ is near but above the critical point λc, and the expected infection time χ(λ) behaves like (λc - λ) with γ = 1 when λ is near but below λc. Analogous results for the oriented percolation model are also obtained.

Original languageEnglish (US)
Pages (from-to)99-112
Number of pages14
JournalStochastic Processes and their Applications
Volume57
Issue number1
DOIs
StatePublished - May 1995

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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