Multitype Contact Process on Z: Extinction and Interface

Abstract

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 (-infinity, L) and (L, infinity). Additionally, we show that if both types are present in finite number in the initial configuration, then there is a positive probability that they are both present for all times. Finally, it is shown that, starting from the configuration in which all sites in (-infinity,0] are occupied by type 1 particles and all sites in (0, infinity) 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