Lattice Green functions for pedestrians: Exponential decay
Mathematical Physics
2023-03-21 v1 math.MP
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.
Keywords
Cite
@article{arxiv.2303.10754,
title = {Lattice Green functions for pedestrians: Exponential decay},
author = {Wojciech Dybalski and Alexander Stottmeister and Yoh Tanimoto},
journal= {arXiv preprint arXiv:2303.10754},
year = {2023}
}
Comments
55 pages, 1 figure