English

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

R2 v1 2026-06-28T09:23:07.865Z