Asymptotic shape for the contact process in random environment

Details Asymptotic shape for the contact process in random environment Asymptotic shape for the contact process in random environment

2009-10-07

arxiv.org/abs/0910.1230v1

Mathematics

Probability

39 pages, in english. A french version is also available

Scientific paper

The aim of this article is to prove asymptotic shape theorems for the contact process in stationary random environment. These theorems generalize known results for the classical contact process. In particular, if H_t denotes the set of already occupied sites at time t, we show that for almost every environment, when the contact process survives, the set H_t/t almost surely converges to a compact set that only depends on the law of the environment. To this aim, we prove a new almost subadditive ergodic theorem.

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