论文标题
$φ^4_3 $的弱普遍性：多项式潜力和一般平滑机制
Weak universality of $Φ^4_3$: polynomial potential and general smoothing mechanism
论文作者
论文摘要
我们考虑三维圆环上的一类随机反应扩散方程。非线性是弱非线性方案中的奇多项式，平滑机制是laplacian的一般高阶扰动。随机性是没有正则化的时空白噪声。我们表明，这些过程会收敛到动态$φ^4_3（λ）$模型，其中耦合常数$λ$具有显式表达式，涉及平滑机制和非线性的所有细节之间的非平凡相互作用。
We consider a class of stochastic reaction-diffusion equations on the three dimensional torus. The non-linearities are odd polynomials in the weakly non-linear regime, and the smoothing mechanisms are very general higher order perturbations of the Laplacian. The randomness is the space-time white noise without regularisation. We show that these processes converge to the dynamical $Φ^4_3 (λ)$ model, where the coupling constant $λ$ has an explicit expression involving non-trivial interactions between all details of the smoothing mechanism and the non-linearity.
