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arXiv · 1004.1951

Tightness for the interface of the one-dimensional contact process

Enrique Andjel·Thomas Mountford·Leandro P. R. Pimentel·Daniel Valesin
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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 $(-\infty,0]$ have Infection 1 and sites in $[1,\infty)$ 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].

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Enrique Andjel, Thomas Mountford, Leandro P. R. Pimentel, Daniel Valesin. 2010-11-23. Tightness for the interface of the one-dimensional contact process. https://doi.org/10.3150/09-bej236

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