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July 2014 Large deviations for the contact process in random environment
Olivier Garet, Régine Marchand
Ann. Probab. 42(4): 1438-1479 (July 2014). DOI: 10.1214/13-AOP840


The asymptotic shape theorem for the contact process in random environment gives the existence of a norm $\mu$ on $\mathbb{R}^{d}$ such that the hitting time $t(x)$ is asymptotically equivalent to $\mu(x)$ when the contact process survives. We provide here exponential upper bounds for the probability of the event $\{\frac{t(x)}{\mu(x)}\notin[1-\varepsilon,1+\varepsilon]\}$; these bounds are optimal for independent random environment. As a special case, this gives the large deviation inequality for the contact process in a deterministic environment, which, as far as we know, has not been established yet.


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Olivier Garet. Régine Marchand. "Large deviations for the contact process in random environment." Ann. Probab. 42 (4) 1438 - 1479, July 2014.


Published: July 2014
First available in Project Euclid: 3 July 2014

zbMATH: 1372.60139
MathSciNet: MR3262483
Digital Object Identifier: 10.1214/13-AOP840

Primary: 60K35
Secondary: 82B43

Keywords: almost subadditive ergodic theorem , asymptotic shape theorem , contact process , large deviation inequalities , random environment , Random growth

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 4 • July 2014
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