0429073 20240103204332.020140819235959.9 000341096600001 84903279685 10.1214/EJP.v19-2904 46 s. E cav_un_epca*00419541083-6489191 (2014)Institute of Mathematical Statistics contact process exponential growth rate eigenmeasure Campbell law Palm law quasi-invariant law cav_un_auth*0244526 Sturm A. DE 50 cav_un_auth*0217893 Swart Jan M. Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics 50 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2014/SI/swart-0429073.pdf GA201/09/1931 GA ČR cav_un_auth*0254026 GAP201/12/2613 GA ČR cav_un_auth*0291241 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. 2015 BA 2 4 A 4a 20231122140304.0 RVO:67985556 http://hdl.handle.net/11104/0235490 S STATISTICSPROBABILITY 1.381 1.704 Q1 70.138 41.393 Q2 Q1 2014 Soubory v repozitáři: swart-0429073.pdf 84903279685 SCOPUS 000341096600001 WOS cav_un_epca*0041954 Electronic Journal of Probability 1083-6489 1083-6489 Roč. 19 č. 1 2014 , 53-1-53-46 Institute of Mathematical Statistics