动力学$Φ_3^4$模型的格点近似
Lattice approximation to the dynamical $Φ_3^4$ model
摘要：
本文研究了[GIP 13]中提出的准控制分布对动力学$Φ^4_3$模型的格点逼近。我们证明了格点系统的解在时间上局部地依概率收敛到动力学$Φ_3^4$模型的解。动力学$Φ_3^4$模型在经典意义上没有很好的定义。为了定义非线性项，必须进行重正化。形式上，这种重正化对应于在方程中增加一个无限质量项，这导致在晶格系统中增加一个漂移项。
英文摘要：
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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