The contact process in a dynamic random environment

Details The contact process in a dynamic random environment The contact process in a dynamic random environment

2009-01-16

arxiv.org/abs/0901.2480v1

Annals of Applied Probability 2008, Vol. 18, No. 6, 2392-2420

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP528 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP528

We study a contact process running in a random environment in $\mathbb {Z}^d$ where sites flip, independently of each other, between blocking and nonblocking states, and the contact process is restricted to live in the space given by nonblocked sites. We give a partial description of the phase diagram of the process, showing in particular that, depending on the flip rates of the environment, survival of the contact process may or may not be possible for large values of the birth rate. We prove block conditions for the process that parallel the ones for the ordinary contact process and use these to conclude that the critical process dies out and that the complete convergence theorem holds in the supercritical case.

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