Survival of Threshold Contact Processes

We consider the d-dimensional threshold contact process. Suppose that a vacant site becomes occupied at rate one when there are at least occupied sites in its neighborhood, and the death rate at any site is >0. We will explicitly give two integers ab with the following properties: For a the process survives starting from finite configurations when is small, but for >a the process dies out starting from any finite configuration with any positive death rate. For b the process has a nontrivial invariant measure when is small, but for >b the only invariant measure is the all-zero configuration for any positive death rate.