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August 2012 Asymptotic shape for the contact process in random environment
Olivier Garet, Régine Marchand
Ann. Appl. Probab. 22(4): 1362-1410 (August 2012). DOI: 10.1214/11-AAP796

Abstract

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.

Citation

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Olivier Garet. Régine Marchand. "Asymptotic shape for the contact process in random environment." Ann. Appl. Probab. 22 (4) 1362 - 1410, August 2012. https://doi.org/10.1214/11-AAP796

Information

Published: August 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1277.60175
MathSciNet: MR2985164
Digital Object Identifier: 10.1214/11-AAP796

Subjects:
Primary: 60K35
Secondary: 82B43

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.22 • No. 4 • August 2012
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