Survival and coexistence for a multitype contact process
J. Theodore Cox and Rinaldo B. Schinazi
Source: Ann. Probab.
Volume 37, Number 3
(2009), 853-876.
Abstract
We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside of this interval.
Primary Subjects: 60K35, 60G57
Secondary Subjects: 60F05, 60J80
Keywords: Contact process; trees; multitype; survival; coexistence; complete convergence
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1245434022
Digital Object Identifier: doi:10.1214/08-AOP422
Zentralblatt MATH identifier:
05587817
References
[1] Chan, B. and Durrett, R. (2006). A new coexistence result for competing contact processes. Ann. Appl. Probab. 16 1155–1165.
[2] Durrett, R. and Neuhauser, C. (1997). Coexistence results for some competition models. Ann. Appl. Probab. 7 10–45.
[3] Häggström, O. and Pemantle, R. (2000). Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model. Stochastic Process. Appl. 90 207–222.
[4] Harris, T. E. (1974). Contact interactions on a lattice. Ann. Probab. 2 969–988.
[5] Kordzakhia, G. and Lalley, S. P. (2005). A two-species competition model on ℤd. Stochastic Process. Appl. 115 781–796.
[6] Liggett, T. M. (1985). Interacting Particle Systems. Springer, Berlin.
[7] Liggett, T. M. (1999). Stochastic Interacting Systems: contact, Voter and Exclusion Processes. Springer, Berlin.
[8] Neuhauser, C. (1992). Ergodic theorems for the multitype contact process. Probab. Theory Related Fields 91 467–506.
