Journal of Statistical Physics

, Volume 139, Issue 3, pp 506–517 | Cite as

Contact Process in a Wedge

  • J. Theodore Cox
  • Nevena Marić
  • Rinaldo Schinazi


We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor “grass-bushes-trees” successional model introduced in Durrett and Swindle (Stoch. Proc. Appl. 37:19–31, 1991).


Contact process Grass-bushes-trees 


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  1. 1.
    Alarcon, T., Byrne, H.M., Maini, P.K.: A cellular automaton for tumour growth in inhomogeneous environment. J. Theor. Biol. 225, 257–274 (2003) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Campanino, M., Klein, A.: Decay of two-point functions for (d+1)-dimensional percolation, Ising and Potts models with d-dimensional disorder. Commun. Math. Phys. 135, 489–497 (1991) ADSGoogle Scholar
  3. 3.
    Chayes, J.T., Chayes, L.: Critical points and intermediate phases on wedges of ℤd. J. Phys. A, Math. Gen 19, 3033–3048 (1986) MATHCrossRefMathSciNetADSGoogle Scholar
  4. 4.
    Durrett, R., Swindle, G.: Are there bushes in a forest? Stoch. Proc. Appl 37, 19–31 (1991) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Grimmett, G.: Bond percolation on subsets of the square lattice, and the transition between one-dimensional and two-dimensional behavior. J. Phys. A, Math. Gen 16, 599–604 (1983) MATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Harris, T.E.: Contact interactions on a lattice. Ann. Probab. 2, 969–988 (1974) MATHCrossRefGoogle Scholar
  7. 7.
    Liggett, T.M.: Interacting Particle Systems. Springer, Berlin (1985) MATHGoogle Scholar
  8. 8.
    Liggett, T.M.: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin (1999) MATHGoogle Scholar
  9. 9.
    Madras, N., Schinazi, R., Schonmann, R.: On the critical behavior of the contact process in deterministic inhomogeneous environments. Ann. Probab. 22, 1140–1159 (1994) MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    McCoy, B., Wu, T.T.: Theory of the two-dimensional Ising model with random impurities. I. Thermodynamics. Phys. Rev. B 76, 631–643 (1968) MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • J. Theodore Cox
    • 1
  • Nevena Marić
    • 2
  • Rinaldo Schinazi
    • 3
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of Mathematics and CSUniversity of Missouri- St. LouisSt. LouisUSA
  3. 3.Department of MathematicsUniversity of Colorado-Colorado SpringsColorado SpringsUSA

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