Multitype Contact Process on: Extinction and Interface

Original · EN

We consider a two-type contact process on 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 (-∞, L) and (L, ∞). We also show that, starting from the configuration in which all sites in (-∞, 0] are occupied by type 1 particles and all sites in (0, ∞) are occupied by type 2 particles, the process ρₜ defined by the size of the interface area between the two types at time t is tight.