Lattice approximation to the dynamical $Φ_3^4$ model

Rongchan Zhu; Xiangchan Zhu

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arXiv · 1508.05613

Lattice approximation to the dynamical $Φ_3^4$ model

Rongchan Zhu·Xiangchan Zhu

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Abstract

We study the lattice approximations to the dynamical $Φ^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $Φ_3^4$ model in probability, locally in time. The dynamical $Φ_3^4$ 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.

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BibTeX RIS

Rongchan Zhu, Xiangchan Zhu. 2015-08-23. Lattice approximation to the dynamical $Φ_3^4$ model. https://arxiv.org/abs/1508.05613

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