Invariant Measures for Spatial Contact Model in Small Dimensions

#### Yu.G. Kondratiev, O.V. Kutoviy, S.A. Pirogov, E. Zhizhina

2021, v.27, Issue 3, 413-438

ABSTRACT

We study invariant measures of continuous contact model in small dimensional
spaces ($d =1,2$). We prove that this system has the one-parameter set of invariant measures
in the critical regime provided the dispersal kernel has a heavy tail. The convergence
to these invariant measures for a broad class of initial states is established.

Keywords: birth-and-death process; dispersal kernel; heavy tail distribution; Markov process; correlation functions