## Bernoulli

• Bernoulli
• Volume 16, Number 4 (2010), 909-925.

### Tightness for the interface of the one-dimensional contact process

#### Abstract

We consider a symmetric, finite-range contact process with two types of infection; both have the same (supercritical) infection rate and heal at rate 1, but sites infected by Infection 1 are immune to Infection 2. We take the initial configuration where sites in $(−∞, 0]$ have Infection 1 and sites in $[1, ∞)$ have Infection 2, then consider the process $ρ_t$ defined as the size of the interface area between the two infections at time $t$. We show that the distribution of $ρ_t$ is tight, thus proving a conjecture posed by Cox and Durrett in [Bernoulli 1 (1995) 343–370].

#### Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 909-925.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092889

Digital Object Identifier
doi:10.3150/09-BEJ236

Mathematical Reviews number (MathSciNet)
MR2759162

Zentralblatt MATH identifier
1209.60053

Keywords
contact process interfaces

#### Citation

Andjel, Enrique; Mountford, Thomas; Pimentel, Leandro P.R.; Valesin, Daniel. Tightness for the interface of the one-dimensional contact process. Bernoulli 16 (2010), no. 4, 909--925. doi:10.3150/09-BEJ236. https://projecteuclid.org/euclid.bj/1290092889

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