Construction of ${\Phi }_3^4$ diagrams for pedestrians

Abstract

We aim to give a pedagogic and essentially self-contained presentation of the construction of various stochastic objects appearing in the dynamical ${\Phi }_3^4$ model. The construction presented here is based on the use of paraproducts. The emphasis is on describing the stochastic objects themselves rather than introducing a solution theory for the equation.

arXiv comment39 pages

References in corpus (3)

• An analytic BPHZ theorem for regularity structures
• Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations
• Renormalization Group and Stochastic PDE's

Cited by in corpus (7)

• A variational method for ${\Phi }_3^4$
• Global solutions to elliptic and parabolic ${\Phi }^4$ models in Euclidean space
• Weak universality for a class of 3d stochastic reaction-diffusion models
• A Stochastic Model of Chemorepulsion with Additive Noise and Nonlinear Sensitivity
• Random initial conditions for semi-linear PDEs
• An introduction to singular SPDEs
• Smooth approximation of Yang--Mills theory on ${\mathbb{R}}^2$: a rough path approach