Weak universality for a class of 3d stochastic reaction-diffusion models

Abstract

We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic ${\Phi }_3^4$ model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular $C^9$ is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their $L^p$ norms in terms of the graphs of the standard ${\Phi }_3^4$ stochastic terms.

arXiv comment51 pages, exposition substantially improved

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• Renormalization Group and Stochastic PDE's
• Large scale behaviour of 3D continuous phase coexistence models
• Central limit theorems for multiple Skorohod integrals
• Construction of ${\Phi }_3^4$ diagrams for pedestrians
• Regularity structures and the dynamical ${\Phi }_3^4$ model
• Weak universality of dynamical ${\Phi }_3^4$: non-Gaussian noise
• Renormalization of the two-dimensional stochastic nonlinear wave equations
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Cited by in corpus (5)

• A variational method for ${\Phi }_3^4$
• The dynamical sine-Gordon model in the full subcritical regime
• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization
• Large-scale limit of interface fluctuation models
• Sharp convergence of nonlinear functionals of a class of Gaussian random fields