Recurrent and (strongly) resolvable graphs
Functional Analysis
2023-01-06 v1 Metric Geometry
Abstract
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool is a connection between polar sets in such boundaries and null sets of paths. This connection relies on suitably diverging functions of finite energy.
Cite
@article{arxiv.2301.01994,
title = {Recurrent and (strongly) resolvable graphs},
author = {Daniel Lenz and Simon Puchert and Marcel Schmidt},
journal= {arXiv preprint arXiv:2301.01994},
year = {2023}
}