The Annals of Applied Probability

Asymptotic shape for the contact process in random environment

Olivier Garet and Régine Marchand

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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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Ann. Appl. Probab., Volume 22, Number 4 (2012), 1362-1410.

First available in Project Euclid: 10 August 2012

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Random growth contact process random environment almost subadditive ergodic theorem asymptotic shape theorem


Garet, Olivier; Marchand, Régine. Asymptotic shape for the contact process in random environment. Ann. Appl. Probab. 22 (2012), no. 4, 1362--1410. doi:10.1214/11-AAP796.

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