Tightness for the interface of the one-dimensional contact process

Enrique Andjel, Thomas Mountford, Leandro P.R. Pimentel, and Daniel Valesin

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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 ρt defined as the size of the interface area between the two infections at time t. We show that the distribution of ρt is tight, thus proving a conjecture posed by Cox and Durrett in [Bernoulli 1 (1995) 343–370].

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

First available in Project Euclid: 18 November 2010

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contact process interfaces


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.

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