Blocking measures for asymmetric exclusion processes via coupling

Abstract

We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of an invariant blocking measure for the first implies the existence of such a measure for the second. The main tool is a coupling between the two processes under which the first dominates the second in an appropriate sense. In an appendix we construct a class of processes for which the existence of a blocking measure can be proven directly; these are candidates for comparison processes in applications of the main result.