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2010 Multitype Contact Process on $\mathbb{Z}$: Extinction and Interface
Daniel Valesin
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Electron. J. Probab. 15: 2220-2260 (2010). DOI: 10.1214/EJP.v15-836

Abstract

We consider a two-type contact process on the integers. Both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is confined to a finite interval and surrounded by infinitely many individuals of the other type. Additionally, we show that if both types are present in finite number in the initial configuration, then there is a positive probability that they are both present for all times. Finally, it is shown that, starting from the configuration in which all sites to the left of the origin are occupied by type 1 particles and all sites to the right of the origin are occupied by type 2 particles, the process defined by the size of the interface area between the two types is stochastically tight.

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Daniel Valesin. "Multitype Contact Process on $\mathbb{Z}$: Extinction and Interface." Electron. J. Probab. 15 2220 - 2260, 2010. https://doi.org/10.1214/EJP.v15-836

Information

Accepted: 18 December 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60137
MathSciNet: MR2748404
Digital Object Identifier: 10.1214/EJP.v15-836

Subjects:
Primary: 60K35

JOURNAL ARTICLE
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Vol.15 • 2010
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