The critical contact process in a randomly evolving environment dies out

Details The critical contact process in a randomly evolving environment dies out The critical contact process in a randomly evolving environment dies out

2007-11-08

arxiv.org/abs/0711.1258v2

Latin American Journal of Probability and Mathematical Statistics, Alea 4, 337-357, 2008

Mathematics

Probability

21 pages, 3 figures

Scientific paper

Bezuidenhout and Grimmett proved that the critical contact process dies out. Here, we generalize the result to the so called contact process in a random evolving environment (CPREE), introduced by Erik Broman. This process is a generalization of the contact process where the recovery rate can vary between two values. The rate which it chooses is determined by a background process, which evolves independently at different sites. As for the contact process, we can similarly define a critical value in terms of survival for this process. In this paper we prove that this definition is independent of how we start the background process, that finite and infinite survival (meaning nontriviality of the upper invariant measure) are equivalent and finally that the process dies out at criticality.

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