The Annals of Probability

Survival and coexistence for a multitype contact process

J. Theodore Cox and Rinaldo B. Schinazi

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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.

Article information

Source
Ann. Probab., Volume 37, Number 3 (2009), 853-876.

Dates
First available in Project Euclid: 19 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1245434022

Digital Object Identifier
doi:10.1214/08-AOP422

Mathematical Reviews number (MathSciNet)
MR2537523

Zentralblatt MATH identifier
1181.60143

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G57: Random measures
Secondary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Contact process trees multitype survival coexistence complete convergence

Citation

Cox, J. Theodore; Schinazi, Rinaldo B. Survival and coexistence for a multitype contact process. Ann. Probab. 37 (2009), no. 3, 853--876. doi:10.1214/08-AOP422. https://projecteuclid.org/euclid.aop/1245434022


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References

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