The exponential decay of lattice Green functions is one of the main technical ingredients of the Bałaban’s approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes–Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation and the method of images.

中文翻译：

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行人的格绿函数：指数衰减

晶格格林函数的指数衰减是Bałaban 重整化方法的主要技术成分之一。我们在这里给出一个独立的证明，其各种成分散布在文献中。指数衰减的主要来源是库姆斯-托马斯方法和傅立叶变换的解析性。使用重整化群方程和图像方法将它们组合起来。