We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero. Therefore, in order to capture the behaviour for an arbitrary small density of particles, we consider a proper rescaling of a model with a typically high number of particles per site. Furthermore, we obtain some results on the convergence for the method of lines for FDE.

中文翻译：

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快速扩散方程的晶格模型

我们获得了一个快速扩散方程 (FDE) 作为具有对称单位速率的零范围过程序列的缩放限制。快速扩散效应来自这样一个事实，即扩散系数随着密度变为零而变大。因此，为了捕捉任意小密度粒子的行为，我们考虑对每个站点通常具有大量粒子的模型进行适当的重新缩放。此外，我们还获得了 FDE 线法收敛性的一些结果。