The Annals of Applied Probability

A new coexistence result for competing contact processes

Benjamin Chan and Richard Durrett

Full-text: Open access

Abstract

Neuhauser [Probab. Theory Related Fields 91 (1992) 467–506] considered the two-type contact process and showed that on ℤ2 coexistence is not possible if the death rates are equal and the particles use the same dispersal neighborhood. Here, we show that it is possible for a species with a long-, but finite, range dispersal kernel to coexist with a superior competitor with nearest-neighbor dispersal in a model that includes deaths of blocks due to “forest fires.”

Article information

Source
Ann. Appl. Probab., Volume 16, Number 3 (2006), 1155-1165.

Dates
First available in Project Euclid: 2 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1159804978

Digital Object Identifier
doi:10.1214/105051606000000132

Mathematical Reviews number (MathSciNet)
MR2260060

Zentralblatt MATH identifier
1110.60089

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Coexistence competition model block construction interacting particle system

Citation

Chan, Benjamin; Durrett, Richard. A new coexistence result for competing contact processes. Ann. Appl. Probab. 16 (2006), no. 3, 1155--1165. doi:10.1214/105051606000000132. https://projecteuclid.org/euclid.aoap/1159804978


Export citation

References

  • Bezuidenhout, C. and Grimmett, G. (1990). The critical contact process dies out. Ann. Probab. 18 1462--1482.
  • Durrett, R. (1995). Ten lectures on particle systems. St. Flour Lecture Notes. Lecture Notes in Math. 1608 97--201. Springer, New York.
  • Durrett, R. and Griffeath, D. (1982). Contact processes in several dimensions. Z. Wahrsch. Verw. Gebiete 59 535--552.
  • Harris, T. E. (1972). Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. in Math. 9 66--89.
  • Levin, S. A. (1970). Community equilibria and stability, and an extension of the competitive exclusion principle. American Naturalist 104 413--423.
  • Liggett, T. M. (1999). Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin.
  • Neuhauser, C. (1992). Ergodic theorems for the multitype contact process. Probab. Theory Related Fields 91 467--506.
  • Pacala, S. W., Canham, C. D., Saponara, J., Silander, J. A. Jr., Krobe, R. K. and Ribbens, E. (1996). Forest models defined by field measurements: Estimation, error analyis and dynamics. Ecological Monographs 66 1--43.