# Lattice approximation to the dynamical $\Phi_3^4$ model

@article{Zhu2015LatticeAT,
title={Lattice approximation to the dynamical \$\Phi\_3^4\$ model},
author={Rongchan Zhu and Xiangchan Zhu},
journal={arXiv: Probability},
year={2015}
}
• Published 23 August 2015
• Mathematics, Physics
• arXiv: Probability
We study the lattice approximations to the dynamical $\Phi^4_3$ 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…
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