# 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} }

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…

## 17 Citations

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- MathematicsScience China Mathematics
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We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved…

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