N. Madras et al., ON THE CRITICAL-BEHAVIOR OF THE CONTACT PROCESS IN DETERMINISTIC INHOMOGENEOUS ENVIRONMENTS, Annals of probability, 22(3), 1994, pp. 1140-1159
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.