## Electronic Journal of Probability

### Multitype Contact Process on $\mathbb{Z}$: Extinction and Interface

Daniel Valesin

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 73, 2220-2260.

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

https://projecteuclid.org/euclid.ejp/1464819858

Digital Object Identifier
doi:10.1214/EJP.v15-836

Mathematical Reviews number (MathSciNet)
MR2748404

Zentralblatt MATH identifier
1226.60137

Keywords
Interacting Particle Systems

Rights

#### Citation

Valesin, Daniel. Multitype Contact Process on $\mathbb{Z}$: Extinction and Interface. Electron. J. Probab. 15 (2010), paper no. 73, 2220--2260. doi:10.1214/EJP.v15-836. https://projecteuclid.org/euclid.ejp/1464819858

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