An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.

中文翻译：

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关于局部相互作用布朗粒子的宏观极限

考虑了由具有局部相互作用的扩散过程组成的相互作用粒子系统，并研究了非线性PDE的宏观极限。在这个问题上几乎没有严格的结果，尤其是非线性的显式形式是未知的。本文回顾了该主题，并介绍了获得极限非线性PDE的一些主要思想，并提供了关于非线性精确形式的启发式和数值信息，这对文献而言是新的，并且与少数已知信息相一致。