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arXiv · 2301.01994

Recurrent and (strongly) resolvable graphs

Daniel Lenz·Simon Puchert·Marcel Schmidt
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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.

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Daniel Lenz, Simon Puchert, Marcel Schmidt. 2023-01-05. Recurrent and (strongly) resolvable graphs. https://arxiv.org/abs/2301.01994

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