On Projections of the Supercritical Contact Process: Uniform Mixing and Cutoff Phenomenon

We consider the contact process on a countable-infinite and connected graph of bounded degree. Our focus is on its mixing properties in the supercritical regime. In particular, we prove that the projection of the stationary contact process onto a finite subset forms a process which is ϕ-mixing whenever the infection parameter is sufficiently large. The proof of this is based on large deviation estimates for the spread of an infection and general correlation inequalities. In the special case of the contact process on ℤ^d, d ≥ 1, we furthermore show the cutoff phenomenon, valid in the entire supercritical regime.