Large deviations for the contact process in random environment

Olivier Garet; Régine Marchand

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arXiv · 1203.2007

Large deviations for the contact process in random environment

Olivier Garet·Régine Marchand

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Abstract

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm $\mu$ on $\Rd$ 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 $\{\frac{t(x)}{\mu(x)}\not\in [1-\epsilon,1+\epsilon]\}$; 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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BibTeX RIS

Olivier Garet, Régine Marchand. 2012-03-09. Large deviations for the contact process in random environment. https://arxiv.org/abs/1203.2007

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