Advertisement

Contact processes in several dimensions

  • Richard Durrett
  • David Griffeath
Article

Keywords

Stochastic Process Probability Theory Mathematical Biology Contact Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Biggins, J.D.: The asymptotic shape of the branching random walk. Advances Appl. Probab. 10, 62–84 (1978)Google Scholar
  2. 2.
    Bramson, M., Griffeath, D.: On the Williams-Bjerknes tumor growth model. I. Ann. Probab. 9, 173–185 (1981)Google Scholar
  3. 3.
    Bramson, M., Griffeath, D.: On the Williams-Bjerknes tumor growth model: II. Math. Proc. Cambridge. Philos. Soc. 88, 339–357 (1980)Google Scholar
  4. 4.
    Cox, J.T., Durrett, R.: Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Probab. 9, 583–603 (1981)Google Scholar
  5. 5.
    Durrett, R.: On the growth of one dimensional contact processes. Ann. Probab. 8, 890–907 (1980)Google Scholar
  6. 6.
    Durrett, R.: An introduction to infinite particle systems. Stochastic Processes and their Applications 11, 109–150 (1981)Google Scholar
  7. 7.
    Durrett, R., Griffeath, D.: Supercritical contact processes on Z. Ann. Probab. [To appear 1982]Google Scholar
  8. 8.
    Durrett, R., Liggett, T.: The shape of the limit set in Richardson's growth model. Ann. Probab. 9, 186–193 (1981)Google Scholar
  9. 9.
    Griffeath, D.: Additive and Cancellative Interacting Particle Systems. Lecture Notes in Mathematics 724. New York-Berlin-Heidelberg: Springer, 1979Google Scholar
  10. 10.
    Griffeath, D.: The basic contact processes. Stochastic Processes and their Applications 11, 151–185 (1981)Google Scholar
  11. 11.
    Hammersley, J.: Postulates for subadditive processes. Ann. Probab. 2, 652–680 (1974)Google Scholar
  12. 12.
    Harris, T.E.: Contact interactions on a lattice. Ann. Probab. 2, 969–988 (1974)Google Scholar
  13. 13.
    Harris, T.E.: On a class of set-valued Markov processes. Ann. Probab. 4, 175–194 (1976)Google Scholar
  14. 14.
    Harris, T.E.: Additive set-valued Markov processes and graphical methods. Ann. Probab. 6, 355–378 (1978)Google Scholar
  15. 15.
    Kesten, H.: Contribution to the discussion of [17]., 903 (1973)Google Scholar
  16. 16.
    Holley, R., Liggett, T.: The survival of contact processes. Ann Probab. 6, 198–206 (1978)Google Scholar
  17. 17.
    Kingman, J.F.C.: Subadditive ergodic theory. Ann. Probab. 1, 883–909 (1973)Google Scholar
  18. 18.
    Richardson, D.: Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74, 515–528 (1973)Google Scholar
  19. 19.
    Rost, H.: Nonequilibrium behavior of a many particle process: density profile and local equilibria. Z. Wahrscheinlichkeitstheorie verw. Gebiete 58, 41–54 (1981)Google Scholar
  20. 20.
    Schürger, K.: On the asymptotic geometrical behavior of a class of contact interaction processes with a monotone infection rate. Z. Wahrscheinlichkeitstheorie verw. Gebiete 48, 35–48 (1979)Google Scholar
  21. 21.
    Williams, T., Bjerknes, R.: Stochastic model for abnormal clone spread through epithelial basal layer. Nature 236, 19–21 (1972)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Richard Durrett
    • 1
  • David Griffeath
    • 2
  1. 1.Mathematics DepartmentUniversity of CaliforniaLos AngelesUSA
  2. 2.Mathematics DepartmentUniversity of Wisconsin, Van Vleck HallMadisonUSA

Personalised recommendations