@article{EJP2904,
author = {Anja Sturm and Jan Swart},
title = {Subcritical contact processes seen from a typical infected site},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Contact process, exponential growth rate, eigenmeasure, Campbell law, Palm law, quasi-invariant law.},
abstract = {What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved under the dynamics up to a time-dependent exponential factor. In this paper, we study eigenmeasures of contact processes on general countable groups in the subcritical regime. We prove that in this regime, the process has a unique spatially homogeneous eigenmeasure. As an application, we show that the law of the process as seen from a typical infected site, chosen according to a Campbell law, converges to a long-time limit. We also show that the exponential decay rate of the expected number of infected sites is continuously differentiable and strictly increasing as a function of the recovery rate, and we give a formula for the derivative in terms of the long time limit law of the process as seen from a typical infected site.},
pages = {no. 53, 1-46},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2904},
url = {http://ejp.ejpecp.org/article/view/2904}}