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arxiv: 1004.1958 · v1 · submitted 2010-04-12 · 🧮 math.PR

Multitype Contact Process on Z: Extinction and Interface

classification 🧮 math.PR
keywords inftytypeprocesssitesconfigurationcontactfiniteinterface
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We consider a two-type contact process on $\Z$ in which both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is confined to a finite interval $[-L,L]$ and the other type occupies infinitely many sites both in $(-\infty, L)$ and $(L, \infty)$. We also show that, starting from the configuration in which all sites in $(-\infty, 0]$ are occupied by type 1 particles and all sites in $(0, \infty)$ are occupied by type 2 particles, the process $\rho_t$ defined by the size of the interface area between the two types at time $t$ is tight.

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