Large deviations for the dynamic $\Phi^{2n}_d$ model
Résumé
We are dealing with the validity of a large deviation principle for a class of reaction-diffusion equations with polynomial non-linearity, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $ǫ$ and $δ(ǫ$), respectively, with $0 < ǫ, δ(ǫ) << 1$. We prove that, under the assumption that $ǫ$ and $δ(ǫ)$ satisfy a suitable scaling limit, a large deviation principle holds in the space of continuous trajectories with values both in the space of square-integrable functions and in Sobolev spaces of negative exponent. Our result is valid, without any restriction on the degree of the polynomial nor on the space dimension.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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