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Article Dans Une Revue Applied Mathematics and Optimization Année : 2019

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

Arnaud Debussche
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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.
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Dates et versions

hal-01518465 , version 1 (04-05-2017)

Identifiants

Citer

Sandra Cerrai, Arnaud Debussche. Large deviations for the dynamic $\Phi^{2n}_d$ model. Applied Mathematics and Optimization, 2019, 80 (1), pp.81-102. ⟨10.1007/s00245-017-9459-4⟩. ⟨hal-01518465⟩
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