Inhomogeneous voter models in one dimension (Q1397958)

The paper investigates spatially inhomogeneous, one-dimensional voter models and establishes conditions for survival and extinction. First, it is shown that increasing the flip rates at a finite number of sites typically does not affect survival, unless the flip mechanism is altered. The proof is based on a coupling of the process with a spatially inhomogeneous random walk in the plane. Second, a modified voter model is constructed and a condition for survival is provided in terms of a single parameter \(c>0\). The process survives if and only if \(c>1\). The critical process at \(c=1\) does not survive but can be made to survive simply by altering the flip mechanism at one side. The proof for the behavior at the critical point is based on a connection with one-dimensional random walks. Finally, it is shown that a rather general class of such models exhibits clustering behavior.