ON THE CRITICAL-BEHAVIOR OF THE CONTACT PROCESS IN DETERMINISTIC INHOMOGENEOUS ENVIRONMENTS

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 th e 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 smalle r than 1, then the critical point is identical to that of the homogene ous system. Extensions of the results to other (d + 1)-dimensional sys tems with d-dimensional deterministic inhomogeneities are also discuss ed.