Weak universality of dynamical ${\Phi }_3^4$: non-Gaussian noise

Abstract

We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrability and mixing conditions, but not necessarily Gaussian. We show that, in the weakly nonlinear regime, if the external potential is a symmetric polynomial and a certain average of it exhibits pitchfork bifurcation, then these models all rescale to ${\Phi }_3^4$ near their critical point.

37 pages; updated introduction and references

References in corpus (3)

• The one-dimensional KPZ equation and its universality class
• A central limit theorem for the KPZ equation
• Large scale behaviour of 3D continuous phase coexistence models

Cited by in corpus (5)

• An analytic BPHZ theorem for regularity structures
• Flow equation approach to singular stochastic PDEs
• Weak universality for a class of 3d stochastic reaction-diffusion models
• Large-scale limit of interface fluctuation models
• Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits