The contact process

  • Nicolas Lanchier
Chapter
First Online:
Part of the Universitext book series (UTX)

Abstract

In this chapter, we prove that, similarly to the other invasion models introduced in this textbook, the contact process exhibits a phase transition: There is a critical birth parameter above which the process starting with one individual survives with positive probability but below which it goes extinct eventually with probability one.

Keywords

Invariant Measure Single Individual Death Process Dual Process Contact Process 
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References

  1. 5.
    C. Bezuidenhout and G. Grimmett. The critical contact process dies out. Ann. Probab., 18(4):1462–1482, 1990.MathSciNetCrossRefMATHGoogle Scholar
  2. 6.
    C. Bezuidenhout and G. Grimmett. Exponential decay for subcritical contact and percolation processes. Ann. Probab., 19(3):984–1009, 1991.MathSciNetCrossRefMATHGoogle Scholar
  3. 30.
    R. Durrett and C. Neuhauser. Epidemics with recovery in D = 2. Ann. Appl. Probab., 1(2):189–206, 1991.MathSciNetCrossRefMATHGoogle Scholar
  4. 75.
    C. Neuhauser. Ergodic theorems for the multitype contact process. Probab. Theory Related Fields, 91(3–4):467–506, 1992.MathSciNetCrossRefMATHGoogle Scholar
  5. 82.
    R. Pemantle. The contact process on trees. Ann. Probab., 20(4):2089–2116, 1992.MathSciNetCrossRefMATHGoogle Scholar
  6. 89.
    R. B. Schinazi. Classical and spatial stochastic processes. Birkhäuser Boston, Boston, MA, 1999.CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nicolas Lanchier
    • 1
  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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