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The Complete Convergence Theorem Holds for Contact Processes on Open Clusters of ℤd×ℤ+

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Abstract

We study contact processes on open clusters of half space. Our result shows that the complete convergence theorem holds.

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References

  1. Bezuidenhout, C., Grimmett, G.: The critical contact process dies out. Ann. Probab. 18, 1462–1482 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bramson, M., Durrett, R., Schonmann, R.H.: The contact process in a random environment. Ann. Probab. 19, 960–983 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Durrett, R.: Oriented percolation in two dimensions. Ann. Probab. 12, 999–1040 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Durrett, R.: Lecture Notes on Particle Systems and Percolation. Wadsworth, Pacific Grove (1988)

    MATH  Google Scholar 

  5. Griffeath, D.: The basic contact processes. Stoch. Process. Appl. 11, 151–185 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  6. Grimmett, G.: Percolation, 2nd edn. Springer, Berlin (1999)

    MATH  Google Scholar 

  7. Harris, T.E.: Contact interactions on a lattice. Ann. Probab. 2, 969–988 (1974)

    Article  MATH  Google Scholar 

  8. Harris, T.E.: Additive set-valued Markov processes and graphical methods. Ann. Probab. 6, 355–378 (1978)

    Article  MATH  Google Scholar 

  9. Klein, A.: Extinction of contact and percolation processes in a random environment. Ann. Probab. 22, 1227–1251 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liggett, T.M.: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin (1999)

    MATH  Google Scholar 

  11. Pemantle, R., Stacey, A.M.: The branching random walk and contact process on Galton-Watson and nonhomogeneous trees. Ann. Probab. 29, 1563–1590 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Richardson, D.: Random growth in a tessellation. Proc. Camb. Philos. Soc. 74, 515–528 (1973)

    Article  MATH  Google Scholar 

  13. Steif, J.E., Warfheimer, M.: The critical contact process in a randomly evolving environment dies out. Preprint

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, China

    Xinxing Chen & Qiang Yao

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  1. Xinxing Chen
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  2. Qiang Yao
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Correspondence to Xinxing Chen.

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Chen, X., Yao, Q. The Complete Convergence Theorem Holds for Contact Processes on Open Clusters of ℤd×ℤ+ . J Stat Phys 135, 651–680 (2009). https://doi.org/10.1007/s10955-009-9756-7

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  • DOI: https://doi.org/10.1007/s10955-009-9756-7

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