On the Critical Behavior of the Contact Process in Deterministic Inhomogeneous Environments

Abstract

We consider the contact process with inhomogeneous deterministic death rates. We prove the following: 1. Such models may have discontinuous transitions, in the sense of surviving at the critical point. 2. If the death rates are identically 1, except on a set which is small enough in a proper sense and where the death rates take a fixed value smaller than 1, then the critical point is identical to that of the homogeneous system. Extensions of the results to other $(d + 1)$-dimensional systems with $d$-dimensional deterministic inhomogeneities are also discussed.