Tightness for the interface of the one-dimensional contact process

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

2010-04-12

arxiv.org/abs/1004.1951v2

Bernoulli 2010, Vol. 16, No. 4, 909-925

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/09-BEJ236 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ236

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

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