## The Annals of Probability

### Large deviations for the contact process in random environment

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 42, Number 4 (2014), 1438-1479.

Dates
First available in Project Euclid: 3 July 2014

https://projecteuclid.org/euclid.aop/1404394069

Digital Object Identifier
doi:10.1214/13-AOP840

Mathematical Reviews number (MathSciNet)
MR3262483

Zentralblatt MATH identifier
1372.60139

#### Citation

Garet, Olivier; Marchand, Régine. Large deviations for the contact process in random environment. Ann. Probab. 42 (2014), no. 4, 1438--1479. doi:10.1214/13-AOP840. https://projecteuclid.org/euclid.aop/1404394069

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