We consider nearest-neighbour two-dimensional Potts models, with boundary conditions leading to the presence of an interface along the bottom wall of the box. We show that, after a suitable diffusive scaling, the interface weakly converges to the standard Brownian excursion.

中文翻译：

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沿墙 Potts 接口的不变性原理

我们考虑最近邻二维 Potts 模型，边界条件导致沿盒子底壁存在界面。我们表明，在适当的扩散缩放后，界面弱收敛到标准布朗偏移。