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.

51 pages, exposition substantially improved

References in corpus (4)

• Renormalization Group and Stochastic PDE's
• Central limit theorems for multiple Skorohod integrals
• Construction of ${\Phi }_3^4$ diagrams for pedestrians
• A sophisticated proof of the multiplication formula for multiple Wiener integrals