The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 4 (2012), 1362-1410.
Asymptotic shape for the contact process in random environment
Olivier Garet and Régine Marchand
Full-text: Open access
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.
Article information
Source
Ann. Appl. Probab., Volume 22, Number 4 (2012), 1362-1410.
Dates
First available in Project Euclid: 10 August 2012
Permanent link to this document
https://projecteuclid.org/euclid.aoap/1344614198
Digital Object Identifier
doi:10.1214/11-AAP796
Mathematical Reviews number (MathSciNet)
MR2985164
Zentralblatt MATH identifier
1277.60175
Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]
Keywords
Random growth contact process random environment almost subadditive ergodic theorem asymptotic shape theorem
Citation
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. https://projecteuclid.org/euclid.aoap/1344614198
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