- Volume 16, Number 4 (2010), 909-925.
Tightness for the interface of the one-dimensional contact process
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].
Bernoulli, Volume 16, Number 4 (2010), 909-925.
First available in Project Euclid: 18 November 2010
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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