Invariant measures for spatial contact model in small dimensions

Abstract

We study invariant measures of continuous contact model in small dimensional spaces ($d=1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of invariant measures parametrized by the spatial density of particles. Also for broad class of initial states we prove the convergence to one of these invariant measures.

arXiv admin note: substantial text overlap with arXiv:1601.07841