# Large deviations for the dynamic $\Phi^{2n}_d$ model

2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : 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.
Document type :
Journal articles
Domain :

Cited literature [15 references]

https://hal.archives-ouvertes.fr/hal-01518465
Contributor : Marie-Annick Guillemer <>
Submitted on : Thursday, May 4, 2017 - 4:41:44 PM
Last modification on : Thursday, November 15, 2018 - 11:59:02 AM
Long-term archiving on : Saturday, August 5, 2017 - 1:52:03 PM

### Files

LDP-SRD-bis.pdf
Files produced by the author(s)

### Citation

Sandra Cerrai, Arnaud Debussche. Large deviations for the dynamic $\Phi^{2n}_d$ model. Applied Mathematics and Optimization, Springer Verlag (Germany), 2018, pp.1-22. ⟨10.1007/s00245-017-9459-4⟩. ⟨hal-01518465⟩

Record views