Rigidity of harmonic functions on the supercritical percolation cluster
Probability
2024-04-01 v2 Analysis of PDEs
Abstract
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a Lipschitz bound. These unique-continuation-type results are false on the full lattice and hence the disorder is utilized in an essential way.
Keywords
Cite
@article{arxiv.2303.04736,
title = {Rigidity of harmonic functions on the supercritical percolation cluster},
author = {Ahmed Bou-Rabee and William Cooperman and Paul Dario},
journal= {arXiv preprint arXiv:2303.04736},
year = {2024}
}
Comments
73 pages, 25 figures; v2 minor revisions