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Recurrent and (strongly) resolvable graphs

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.

preprint2023arXivOpen access
Daniel LenzSimon PuchertMarcel Schmidt
math.MGmath.FA
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Daniel LenzSimon PuchertMarcel Schmidt

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