Dynamics of a spin-exchange model

We study a model on the non-negative half line Z+0, {0, 1, 2, …} in which particles created at the origin at rate 1 jump to the right at rate 1. If a particle jumps onto an already occupied site the two particles annihilate each other. In addition, whenever a particle jumps its closest neighbor to the right jumps along with it. We find that the spatial decay rate of the particle density in the stationary state is of order 1√x at distance x from the origin. This model provides an approximation to the dynamics of an anchored Toom interface which can be represented as a spin-exchange model.