We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf–Cole solutions to the KPZ equation.

中文翻译：

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一类重新缩放到 KPZ 的增长模型

我们考虑一大类$1+1$维连续界面增长模型，我们表明，在弱不对称和中间无序状态下，这些模型收敛到 KPZ 方程的 Hopf-Cole 解。