Lattice approximation to the dynamical ${\Phi }_3^4$ model

Abstract

We study the lattice approximations to the dynamical ${\Phi }_3^4$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical ${\Phi }_3^4$ model in probability, locally in time. The dynamical ${\Phi }_3^4$ model is not well defined in the classical sense. Renormalisation has to be performed in order to define the non-linear term. Formally, this renormalisation corresponds to adding an infinite mass term to the equation which leads to adding a drift term in the lattice systems.

References in corpus (3)

• Approximating three-dimensional Navier-Stokes equations driven by space-time white noise
• Renormalization Group and Stochastic PDE's
• Piecewise linear approximation for the dynamical ${\Phi }_3^4$ model

Cited by in corpus (2)

• Stochastic quantization of an Abelian gauge theory
• Piecewise linear approximation for the dynamical ${\Phi }_3^4$ model