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arXiv · 2303.10754

Lattice Green functions for pedestrians: Exponential decay

Wojciech Dybalski·Alexander Stottmeister·Yoh Tanimoto
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Abstract

The exponential decay of lattice Green functions is one of the main technical ingredients of the Ba{\l}aban'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.

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Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto. 2023-03-19. Lattice Green functions for pedestrians: Exponential decay. https://arxiv.org/abs/2303.10754

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